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   "execution_count": 19,
   "metadata": {
    "tags": [
     "remove-cell"
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   "source": [
    "import sys\n",
    "import os\n",
    "if not any(path.endswith('textbook') for path in sys.path):\n",
    "    sys.path.append(os.path.abspath('../../..'))\n",
    "from textbook_utils import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "tags": [
     "remove-cell"
    ]
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   "outputs": [],
   "source": [
    "csv_file = 'data/Full24hrdataset.csv'\n",
    "usecols = ['Date', 'ID', 'region', 'PM25FM', 'PM25cf1', 'RH']\n",
    "full = (pd.read_csv(csv_file, usecols=usecols, parse_dates=['Date'])\n",
    "        .dropna())\n",
    "full.columns = ['date', 'id', 'region', 'pm25aqs', 'pm25pa', 'rh']\n",
    "\n",
    "bad_dates = ['2019-08-21', '2019-08-22', '2019-09-24']\n",
    "GA = full.loc[(full['id'] == 'GA1') & (~full['date'].isin(bad_dates)) , :]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
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   "source": [
    "(sec:linear_multi)=\n",
    "# Multiple Linear Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "So far in this chapter, we've used a single input variable to predict an outcome variable.\n",
    "Now we introduce the *multiple linear model* that uses\n",
    "more than one feature to predict (or describe or explain) the outcome.\n",
    "Having multiple explanatory features can improve our model's fit to the data and improve predictions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
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   "source": [
    "We start by generalizing from a simple linear model to one that includes a second explanatory variable, called $v$. This model is linear in both $x$ and $v$; meaning that for a pair of values for $x$ and $v$, we can describe, explain, or predict $y$ by the linear combination: \n",
    "\n",
    "$$ y \\approx \\theta_0 + \\theta_1 x + \\theta_2 v$$\n",
    "\n",
    "Notice that for a particular value of $v$, say $v^\\star$, we can re-express the preceding equation as:\n",
    "\n",
    "$$ y \\approx (\\theta_0 + \\theta_2 v^\\star) ~+~ \\theta_1 x$$\n",
    "\n",
    "In other words, when we hold $v$ constant at $v^\\star$, we have a simple linear relation between $x$ and $y$ with slope $\\theta_1$ and intercept $\\theta_0 + \\theta_2 v^\\star$. \n",
    "For a different value of $v$, say $v^\\dagger$,  we again have a simple linear relationship between $x$ and $y$. The slope for $x$ remains the same and the only change is the intercept, which is now $\\theta_0 + \\theta_2v^\\dagger$."
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   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
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   "source": [
    "With multiple linear regression, we need to remember to interpret the coefficient $\\theta_1$ of $x$ in the presence of the other variables in the model. Holding fixed the values of the other variables in the model (that's just $v$ in this case), an increase of 1 unit in $x$ corresponds to a $\\theta_1$ change in $y$, on average. One way to visualize this kind of multiple linear relationship is to create facets of scatter plots of $(x, y)$ where in each plot the values of $v$ are roughly the same. We make such a scatter plot for the air quality measurements next, and provide examples of additional visualizations and statistics to examine when fitting a multiple linear model.    "
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  {
   "cell_type": "markdown",
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    "user_expressions": []
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   "source": [
    "The scientists who studied the air quality monitors (see {numref}`Chapter %s <ch:pa>`) were looking for an improved model that incorporated weather factors.\n",
    "One weather variable they examined was a daily measurement for relative humidity.  Let's consider a two-variable linear model to explain the PurpleAir measurements based on the AQS sensor measurements and relative humidity. This model has the following form:\n",
    "\n",
    "$$ PA \\approx \\theta_0 + \\theta_1 AQ + \\theta_2 RH$$\n",
    "\n",
    "where $PA$, $AQ$, and $RH$ refer to the variables: the PurpleAir average daily measurement, AQS measurement, and relative humidity, respectively.\n",
    "\n",
    "For a first step, we make a facet plot to compare the relationship between the two air quality measurements for fixed values of humidity. To do this, we transform relative humidity to a categorical variable so that each facet consists of observations with similar humidity:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "rh_cat = pd.cut(GA['rh'], bins=[43,50,55,60,78], \n",
    "                labels=['<50','50-55','55-60','>60'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "Then we use this qualitative feature to subdivide the data into a two-by-two panel of scatterplots: "
   ]
  },
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   "cell_type": "code",
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INrh4m11bliZbhmHs2rWrSp9HEzJlzZo16NWrF8qXL4/x48eDEaRkZ+vfayhk6x9uVn1KyDa4IyNkG1y8za4tS5PtL7/8giFDhmTI8kPA9+zZg8cee0xd+3n66afVvxt99YcfrtOnT4MDUKxYMZdxlznZeLeXSRL0iJzZ6kHJ+DJyZms8pqHQKGe2oUBd7tmGBnVza3U6s12yZAl69uyJpUuXonjx4hlqZx7bRx99VP2d5Gsk2TJd3zvvvGOrj7tqOmHVqlVL/Y1OWWwXk9lTOnXqpBImZM+e3SNCQrbmvkDutAvZhgZ3o2sVsjUaUX36xEFKH07hVMqJbBMTE9GgQQP06dMH/fv3d+oLM/088cQT6u9Gki3PhXkezPNi7nD79u0Lnh/TbE3p3r272tEOHTpUeUl37NhRkS3PlT2JkG1oXkch29DgbnStQrZGI6pPn5CtPpzCqZRLb+QTJ04oE26RIkVc9mX16tU4duwY7rnnHuTIkcOU/pJsaU4ePnw4zp8/j4YNG2LSpEmoX7++qo9ES9JlyEghW1OGICClQrYBwWeZh4VsQzMUQrahwd3MWi0X1GLatGlgUno6YZFoq1WrpkzW7du3B5PWFy1aVOExduxYTJ06VXlKC9ma+Yr4p1vI1j/crPaUkG1oRkTINjS4m1mrE9meO3dOmYf1SKtWrbyemerRY19m2LBhWLduHei1+9FHH6FJkyYurxrRkWvkyJHKa1qTzZs3O1X3n//8B9u3b/e1GaaVJ74FChQwTb9VFF++fFlZR3LmzGmVJpnSjuTkZBU03jHwiymVmaRU83vYtm0b2B97oZ/EzJkzUbBgQZNq901tQkKCisceERHh24NhVvrq1atITU3V7QgaZt2zNZd9pOWSR4jhKt78hrR+OZEtia5z5866+m3kma1jhXSO4r1eXkXSdrY8L9ZM2652ti+//LJTu2fMmKF0WEWYyMEs07tV+sh2aB9tEm5mFn4s6GOgd8JZDYvIyEjbh+7tt99WCwd7+fvvv8GFLQnOCkI/DsZkz+xkK/PHCm+bvjboXYg6kS3Nt/fdd5+qhan06IjkbndSrlw5cLKaIXPmzMELL7wAekDzA+B4ZssIVzxbljNbM9APXKeZZuRfVh/G2BX7ceDMJVQpFotn76iAdjXS7oQHInO3ncCoRXux82QiyhWKQbfbyqFLkzIeVco920AQ9/1ZuWfrO2ZWfiJL37PlwNDUydXs6NGjFdHyXi2v2piZu3bEiBFo3rw5qlatqu7a9uvXD7ly5bJ5I5P4aaoTb2QrT52bbTOLbDccTsBDI5dnACFHVCQW9m+F0gX03b12heDRhCu44+PFuJ6ckuHnX/vchsa3uDehCtkG930Usg0u3mbXluXJVgP4ypUroMMSTbr8ePbo0QNPPfWUKaQ7YMAA/P7777axpdcxz29Lly6t/rZv3z51z/bw4cPqv7njHjx4sFeTrFz9MXu6uNZvFtmOWrwX/5vzr1OlH3eqg04NSvnd2RmbjuHFiRucnn/pzkro17ayW71Ctn5D7teDQrZ+wWbZh4Rs7YaGZ4z0+H3jjTfUXydPnoy6deuaMnisi45R3EG7cyKi6Zi/691lC9maMlRelQrZeoUoLAqIN3Johkm8kUODu5m1ur36w10td5o8EyXB0YzMnW2FChXMbI/huoVsDYdUl0KzyFbMyLrgN6yQkK1hUPqkSMjWJ7jCorAT2ZJkmWLvyy+/VI5JNBvzf46hG8Oid4DKXrR7927LNFcSEQQ+FOIgFTiGejUI2epFythy4U62h89ext97TiMpOQVNKxRGxaJ5XAKUpc3I9ld/mNnHXRQpIseQjnRisrII2YZmdMza2YamN+5rlTPb4I6InNkGF29/apu3/SSe+WkdklNS1eO8Ev3u/TWUd7+jZGmy3bp1K1588UVdGPMsN2/evLrKhqqQkG1okBeyDQ3uRtcqO1ujEdWnL5x3trwtwOMeeymSJyfWvNlGyFbf8IdnKSHb0IybkG1ocDe6ViFboxHVpy+cybbWoLm4cPWGU0c3v3MXYqMzZmnL0jtbDSEG+d+4caOKjMOAEuEaTkvIVt/kNrqUUWR7IyUVy3afxq4TiShbOAatqxYF79XqkY2HE7D2wDnkz50draoUReE87pNmHD53BUNm78CKPaeRPSoSd1QtitfbV1PPehIxI+sZCePKiBnZOCzN0iQ7W9fIuvRG/uuvv9R5rCYxMTEq8L9ZV37MGnTqFbI1E133uo0gW575/OerFSBpalKmYG7M/29L5MzmmXA/+HMHvl267+Y7nCMKk59piurFY102usu3K7Fi75kMvz1+a1kMfrCmkO2cOZaJjSxk630+7z99CR/9uQMr959FTI4otK1eDC+1qYyvF+/F7K3HkXA5CY3KFcCA9tVQNc74Y0A5s9VJtow92qxZM5QpUwYDBw5UOWWZzu7atWtgCMVwi3UrZOt9cppRwgiyXbIrHk98v9qpecM61cHDHgJYXL6eDJqyNAcNTQGf4bOOconl35mDdH8O28/ViufF7JdaCNkK2ZoxRTzqDMSM3PGrFVh/8FwG/U1uKYRV+zMuJukhPK9fS0SakNNBvJGdh9dpZ3vgwAG0bdsWU6ZMQe3atdUT69evBz2TFy9ejJIlSwb9xQukQiHbQNDz/1kjyNZdtKinW1bAa+2rum3c+kMJ6DgqY0hHFq5bOj+mPXe703Mk5UoD/3Qi2/KFY/BX/1ZCtkK2/k8EP5/0l2zdLRxz54gCF6GOsmxA64DCnPrZPdtjWfrMlue0DGDBBPFaFCctefuECRPQqFGjQPEN6vNCtkGF21aZEWQbrJ0tzcePfbdKpTSzF15VeO+BGkK2QrZBn0T+ki0dk+q8O9dp4ShkG/QhdKrQbYq9P/74wxYSkabkNm3a4NNPP0WDBg1sSuLi4kzL+mMUNEK2RiHpmx4jyDZYZ7Y0VS/eFZ/WwXTCjYqMxJqBbVDIg1MVi4uDlG/vRaCl5czWO4JWMCN7b2VaiSy9s7VKPlu9g+WtnJCtN4TM+d0IslVkFgRv5NuH/AVm/XEUPSY2IVtz3h93WoVsveMdagcp7y28WSJLk+3Zs2fBJO165K677vKadUePHjPLCNmaia573UaRrasajp+/ijMXr6FSsbxuvZK5QWW+W4aLq1AkD6LSvUDoiXnwbFqC9E2HE9Q1n6nrj2L1gbMZqorOHoWt77azPeeup0K2wX2/hGyDi7fZtWVpsjUb3GDrF7I1B3GS1kezd2DRv6fS4p9WLIzX2lezOVsYRbZXkpLx6bxd6srCuUvXERUVicQrSapTPId6677qeLRxxgTvu09eRK9xa3DgzGVVrkjenPiicz1MWnMI0zceU3/j+WwEIsD/i4yMUB6ZN5Jvntn2b1cFz99R0St4QrZeITK0gJCtoXCGXJmQbciHwLgGCNkah6W9prembcX4lQczKG9aoRAm9LpV/c0osh2+cDc+nb8rnSDT4qzaS/aoCKx7s22GyDS9xq3F/O0nM5SLy5cLJ85fdQKDO2DqrFkiFo83LYfL15JVsvgaJVzfx3VUIGRrzvvlTquQbXDxNrs2IVuzEQ6ifiFbc8BuPWwx9p1OM8dqwt3h7g/uUaZXo8j2kdH/YNX+NBMv952urgRO7H0rbitfyNYOd2ewrpDQyDZvrmzYMqidz2AJ2foMWUAPCNkGBJ/lHhaytdyQ+N8gIVv/sfP0ZEjINn0X6tiuBS+3RMUiN1N4tf9iKXYcv+C0A06yMxNrP2oEXq90fkx1cQfXG3pCtt4QMvZ3IVtj8Qy1NiHbUI+AgfUL2RoIpp0qI83I244lYvX+s8idMwqtKhdBsdhcuJ6cgr/+PYWfVx7E0t2n02p2QbauSNJVMIz765TAnK0nlF57oqXObFER+KprA9xVvZjPYAnZ+gxZQA8I2QYEn+UeFrJNH5Lly5cjMTER7du3t9wg6W2QkK1epHwrZ5SD1JeL9mDY3J22yhnzePTjDfH29K04dDbNwYlCr+EcURGoWCwP4mKjcSMlBfXKFADjF+dzzCSSCszYeBSLdp7C9RtpzluPNCqN/fGXMHH1IRw8cwlFYnOhRP5oFMubE80qFkbpgrl9AyC9tJCtX7D5/ZCQrd/QOT2459RFrNiblngjkDkQSIuEbNPRY17bixcv4vvvvw8Ez5A+K2QbGvj1nNkyaEXNd+aCHsf2Uq14LHYcT3Rq+I/dG6Nl5SKh6ZCbWoVsgzscQrbG4D3unwN4Z8Y2LYaL8rPw17oTSIuEbNPRGzFiBKZOnQpmAQqG8MPFyVSwYEHkzJnTZZX8PU+ePIiOjtbVJCFbXTAZXkgP2e6Jv4g2nyxxqjs2VzYkusiHyWs+PZrdYnhbA1EoZBsIer4/K2TrO2aunmj0/gLEX7yW4Sd//RYCaZGQbTp6p0+fVmEav/jiC7Rs2TIQTL0+O3r0aAwbNsxWjqbr9957z5ZH9+DBg+jZsyeYKIHC+M3MRsR8u55EyNYr9KYUINkeS7yOlMgcqFQsjzLn0mxVskA0CsWk5ZWVna0p0BuqVJLH+wYnj1d4fHH64jXUL1MADcoWsCmg5/vK/Wew9ch5FMuXC3dUKQp6wdvL5iPnlf9CdFQKbi9fAOXiCvrWAB2leU+99rvznEr665Gvo0q3RYRs06Hp27cvGCPZnaxduxb58uULBGvbs5MmTVJp/Zgz99ChQ+jWrRt69+6NHj16qDLdu3dXO9qhQ4eCie07duyoyPaBBx4QsjVkBIxTwnBxPX9cjb3xaWeuubJH4vqNVKSkxx1uU60YRj/eQJmu9J7ZMmPPlGeaeo3oZFwv9GmSna0+nIwqZeWd7cEzl9FhxLIMVhn6Cgz9T1r2tGd+WofZW0/YoCiQOzsWvNzKtvik7wLngyb0X/j16dtQp1R+o+Cz6ZGdreGQelXoMnm89tT8+fMV8bmTrl27ujX3eq3ZS4E33ngDhw8fxvjx46FlHSIh169fXz1JoiXpfv3110K2gYJt8PPPT1iPWZuPZ9Cq3WfV/vhxpzrolJ6T1pM38sHTl1A5LhbNKxVGNjMSbwbYdyHbAAH08XErk+17M7fj++X7nXq05s02SLxyA3d+stjpt75tKqNvm0rgtbTqb89W/7SXDnVKYMSj9XxEyXtxObP1jpHRJTySrdGV6dXHLEOtW7dGhw4d8Oqrr2LPnj3KI5re0UWLFlVqxo4dq86Tp0+fLmSrF9gglXMbVMKOcZ+6vRze6eA5fV2QmhtQNUK2AcHn88NWJttuY1Zj6e707FF2PRv7VGMkXk3CixM3OPX3vtrF8WWX+nDnv6Anp7LPIKY/IN7I/iLn33NOZHvmzBls374dDRs2xKlTp1QkIHdSrVo1REVF+Vezh6cGDhyozNdz585FsWLFbMnr7c3Wv/zyC0aOHIlly5bZND3xxBNOWplU4Z9//jG8jf4qTE5ONgUzf9tjxHPnr9zA8KWHsHxfgsrSk5IKJwcnLVdsRHq8xV63lUSf20upZ8asOobdpy4jLjYHHqpdFF0axGHa5nhM2nAChxOuokKh3HiySXHcUcn486tA+89+8dzJjHkQaNv0PB8ZGakcEinPP/+803zfsWMHJk6caNhxkZ42eSpj5fnzyV8HMXH9TTOx1o85z9TDxWspePj7TU5d6920FHo3Lal2tC2Gr3Ha2d5VtRA+vM97jO5AcQ3l81YeUz24FC5cWE8xOJEtPY/79OkDmpCHDBmChQsXulVk5JmtVgk9oIcPH44pU6agdu20sw5tZ0viLFIk7eqHq53t0aNHndraqlUr/Pvvv7rACEYhOp3pHZxgtMeIOt6avg0TVh+2qVJB/h2CGNv/jdbgP55vhv3nLuGFnzci2SFp+1v3VMPgP3dkaFqOqEjM69fclujAiHYboYMfCi5I8+c3/lzNiPbp0aEtFE6cOAH2x14eeughtfDVCFmPPjPLMCsZseYiwWrCM9sHR63IsND8v4al8NFDNVVTn5uwAXPWzVDsAAAgAElEQVS23YzZzTPbuX2b285sP52/GyMX77V1i2e2E3s1NuXM1irYcaGakJBgmffLH1z0LrSdyJYv87Zt29TOliYbTzvbqlWrGraiJ+h0fuK57M8//4waNW6aGF2d2Q4aNAj8OMiZrT+vh7HPOJqNyZ2REam4t1YcklIiUL1EXly+loJdpy6gVP5odGpYGl8t3oM/txx3ImW2jB6c6w6ec2qk/TmvsT3wX5uYkf3Hzp8nrWxGZn/CwRvZH9zNeka8kb0gSwLmjvfuu+9Grly5DBmH119/Hb/99hvGjBmD8uXL23TGxcUhW7ZsePLJJxEbGyveyIagbawSV2e03L1uGtgKefPEOFW2N/6SchZxtQMWsjV2bALVJld/AkXQv+cvXbqk5gdvYGRmEbJ1MbpcwdOMO2PGDJtTkpFmZDpE0fvYUWjOLleuHPbt26fu2WplePVn8ODBXpPXyz1b46fqtRsp2HniAtYfPIcNh8+pfx46dyUteHEq8/Kkomn5ghjzeF3kzu0cBpE5ZV/6ZYPK4uMq3vHb91XHe7O2Z2g4zcgL+7eynBlZdrbGv1+eNFp9Z2sUGkK2RiFpHT1evZHpLEWPX5p3+QLExMSoO6733Xcf6tWr59IMaGb3aDrmak/vik/I1tjR+HXtYQyasQ2Xric7pbvjMa12/Mq7tW+2r4yuTSs4NWDQzO0Ym35FQpVP42cUypMDz91RUUWJ+mX1YYxdsR8HzlxClWKxePaOCmhXI87YzhigTcjWABB9UCFk6wNYYVA0y+9seX+VThEkWC1i05133qlMx5MnT1aBJ8JFhGyNGykSbOP35yuiTUUqIhzoNo1obzpHxeSIwuo324L/tBemwNt+LNFpobburbY2ZxHjWm2uJiFbc/F11C5kG1y8za4tS5Pt5s2b8Z///Edh3KJFC9x///0g0dJLkU5TQraBvX4nT55U15nCUdYfSkDHUctV090lcnf8+x8vNkeNErEZultr0Fx1yZ9cHXHT8oy1b7ZBkbyuY2JbFS8h2+COjJBtcPE2u7YsTbbr1q1D586d1Tnp008/jbZt2yrHJM0jWMg2sNcvnMn28LkraD40LSmFK7J1jBLFcssGtHY6Z+01bi3mb795BYLlGD95fj9z428HNnKunxayNQNV9zqFbIOLt9m1ZWmyvXLlCubNm6eiMzFiE4XRm5iI4LXXXpOdbYBvn9XJloQ5e+txRYaXryejSfmC6NK4rIpvzCwhDQcvwM2z2ZsmY1dEW7tkLGa80NwJsd0nL6LXuDU4cCYtdjJ3s190roemFQoFiG7wHxeyDS7mQrbBxdvs2rI02dqDS2cknt3ySg4DS1AYQpE73wYNGhh2x9bMAZUzW9/Q/WnlQbw5bWva7jU9TCuJNpIMGwFcvn5DeRyrM1v+k3bgdB8nsnCaWTht3/t770ZoUD4tvKajUDedn5KSU1ChSB7LJRjQi5qQrV6kjCknZGsMjlbRImTrYiTolTxr1iwV2YmBLxhRhg5Ter2CQzW4Qra+If/gyOXYeDjBRrbaLtYhIFQaEUekOUm5ui8bnT0Kqwc0d3nP1rcWWbu0kG1wx0fINrh4m12bkK0HhPlxYaxhXgdiFCchW99eR6ubkem8dCE9cbtmGnZlIlY73/T/p27upBOvhsYLrcrhmRa3uLxn6xti1i4tZBvc8RGyDS7eZtcmZGuHMHct+/fvV+nsKlSoAEZ0YiJ3BivQ4hSbPSCB6JedrW/ovfTLRkzfmBZj2hvZpnBzy6wDkSwboc5y761VHC+0roRSeaCOGVwFtfCtRdYuLWQb3PGxCtmanTFHgloE970KRm0eg1pcvHgRvXr1AiNFUYYNG6aStT/77LOKgGfPnh2MNgZUh5Ctb/Ax8Xvv8WtBJyZPZJstMhJJKQxswX1tuqQCC15uiYpF86iY2kK2vmFvxdJWCdd4MvEqxv1zEOsOxCM5NRLZoyKVY90dVYri/rol4S3V8dWkFExYfRCr9p1F7hxRaFu9GNrXLK4WiL5KMHLBCtn6OirWL++RbJnG7rPPPgMTuf/4449gCjuS7apVq8DE8X///bfl74wK2fr3Eh46exnHE65iyvojWLzzlDItZ4uKwPXkFFQtFovoHFFYue+Mk3JFtkWEbP1D3XpPWYFsGR609bDFOJpwxeWVs1fvropnWzlHKrNH8/kJ6zFr8/EMAL//YE10vbWsz6A3en+B8sy3l3ql82Pqc7f7rMvdA0K2hkFpGUUeyZYhGXnt57nnnkP37t0V0fJ/dJBq0qRJhjR4lumRQ0OEbM0ZmUdG/4NV+886KR/9eAMVVlF2tubgHmytViDbxTvj8eQPq1XXXd3v9pZgnRHPar0zR+VZtpcmtxTEpD63+QRp4pUk1H53ntMzeXNlw5ZB7XzS5amwkK1hUFpGkUeyJdEyDjJNyfZkq+WXXbRoEUqVKmWZzrhqiJBt2tnr10v24sd/DuDcpSTkzhmJRuUKoXrxvKhaPBa3FMqDNQfSdqlNKxYGP17e5LP5u/DFwt0ZimWPisC6N9siNjq7kK03AMPkdyuQ7Zi/92MwE1O48dRjkopdH7R3i+i2Y4m4d/gyp98L58mBn3reiqGzd2DNgXPInzu7Mi33b1cFzCX774kLLn9rNuQvtbO1pWGOSEVM9uz4rHMdw+J3C9mGyQTxoZkeyZbexkuXLsWECROUKZm7WkaU6tevHzZu3KiyAOlNnOtDmwwtKmQLfDpvFz5fsAuRDgdbtm9XKtSqn/m4eYb1Sae66Fi/pMdx4Ar/qbFrbHlneQ721n3V8WjjMuo52dka+hqHTJkVyJZJ2Vt+vCh9Z+sck7tFpSIY16OxR4yafLgQPPe1l471SmHj4XNgykcVOjT9xwF3V0WflhVw12dLQEcoe+FvMTmj8Na0bbZ9tnbuS9Jf9EorlMwfHfB4CdkGDKHlFHgkW5qLSbAMbkEpXbq0MiHzRWDSdsZMtroI2QKNP1igPjQRLrxBNLMcyTY9bgUqFInBwpdb6Rra4+ev4szFa6hULK/aDWgiZKsLPssXsgLZEiRaUUYs3I2kdFuwRozlCuXGV10bolrxvB6xXLDjJF6ZvAnnLiepcgwPWr9sQfyy6pDNSUrbqd5aviCG/V9dW2hSe8UNyhZQ/7nu4Ll08k9z29fmlnaMEujACtkGiqD1nveaYo/hG+kotWXLFrVbueWWW/Dwww+jcuXK1uuNixZlZbLdd/oSJqw6iG+X7U//IKRHhVKkqwWkSCNZLYsPPzhRkcCmd9qB51D+ipCtv8hZ6zmrkC1RYfjQNTsPo0qZYki8ekN5JJcrFKPbo/hGSqrysufOlO95q2GLbpqC02Hn3z2RbfF8ucAFpr3weqSKngZg+KP1cH+dEgEPopBtwBBaToFXsrVci31sUFYl2zOXrqPl/xbh4rUbaSZihysOaQEpbn4k7NLKoqIPO1t3wyFk6+OLatHiViJbQmTUPdu5206gz/h1TqhzHrzmwYxcukA0mJDDUTiVaNlZ8uodICEHKkK2gSJoveedyJYhGA8dOqSrpV26dEHOnNZOiZZVyTZDjGNXuWfTyZbmL7Uy543ZdEL+9P+8n9l6e0GEbL0hFB6/Z1ay/d/cnRi1KC3eu72ULRSDWS82Q96c2TB901G8OXWruvbGxWr14vlQODYnFv97yum56sVj8VKbSuIg5eNrnaUjSL344ou6g1Uw2EW+fPl8hDe4xTMz2dqfl0ZFRthMZGUK5sa7M7fhh+UHFNhuc8+mb3lTU9Kco/JH58DEPreiWpzn8y89Iyhkqwcl65fJjGS76+QFtP10qQLf3o1BW3SWLZQbs/u2UL4Ol67dsA0S16R314wDd8X2YvQdW+qWna3154avLRQzsq+IBVjeiNjIZy9dB3PCak4aObJFIltkhDrTotD5o8ft5fHa75vdkq12RssCDcsVBO8cdrutLIrFBm4Co04h2wBfFIs8bmWypUf84l3xOHn+KmqWyofbyrtP0ch15ZJd8dh1IhE7TlzAtA1H0yw6GtsyWxVuHrdwl/r5gt328dHUiHB+fPJ/dTBz4zGcvnQN9coUwOO3lkW+6OyGjpiQraFwWkKZLrLlS5mQkJYJpkCBNG88s4R1JScnI1s21845PLNh8oPoaH3u9ZlxZzts7k58aWcCc3X98L7axdV91wmrDqU7gdjlnk1PiUfTWO8WFfBa+6qGD6eQreGQhkShVcn22Plr6u7s+Stp3sWUe2sXx8gu9V3i1HHUcqw/lDGblWNB++xVDOfInM6OkidXNmw1MHiFu0EVsg3J625qpR7JlqQ3YsQIjB07Vpk1KDExMejduzd69OhhynktswkxBvOyZRkvoTP5Qc+ePXHgQJpptFOnTnj33XeRPbvnFWVmJNtuY1Zj6e74tBfDzUV/3vVb/lpr5bV54PQl8Czq7KVrKn9soZicOJJwWeWRzZPTf49jT2+mkK2p8zZoyq1Kth/P24WvFu91woFX1nh1zV6W7T6Nx8essv3J1bGKo9/Cew/UxNvT0/I620vNkvkw64VmpuMvZGs6xEGvwCPZjhs3DoMHD0bz5s1VeMYcOXIoEuT/HnnkEbz//vuGNZhk+tRTT+Hw4cMqs5Aj2TKCFXe0Q4cOVRmIGNmKZMt7wJ4kWGR75NwVtcqmCTclBdh96gLiYnOpYOn24s2MTHPXjI1HsWjnKSReuYGqxfPisVvLKrPXhkPnUDgmJw6evYSV+9JCJaZ9JGgNy+huXLd0fkwzMFarrwMtZOsrYtYsb1Wy7fPTepc7T/t7ricTr6HXj6ux5VgikmkxTg/XmHbVDSgUkwNXrierf7+axLPZtDlEn4f5/22JAVM2q3mnCf0iJvW5FQ3LFjR9sIRsTYc46BV4JFuSLNPo/f777xka9vHHH+Obb75R2YCMcpBiqrLTp09jwYIFGD16dAayPX/+PBo2bIhJkyahfv00MxGJlqTL4BqhJNv4C9dUJKWtR8+rZtD9n4TJHSSlaYVCGP14Q9udVW9kO2rxXvxv9g6kahFt0v8lJYVmYEWr6eR6s9eukrc/WK8k6pTKj8a3FESNErFBf7GEbIMOuSkVWpVs9exs7/p8KXYev+DSCYpz6YOHauGxJmXA+7fc/fI8t2zhGLSuWhSMBkXZfOQ8Vu8/q0I5tqxcxGnxbAro4iBlFqwh1euRbLl7bNq0Kfr375+hkVps5JkzZ6JqVWPP+/744w8MGTIkA9lq9S1fvhxFixZVbaFpe+rUqSqJfSjJNqPXb/ou08Gtwj4riTeyrfnOXFy4dsOmIU0jvTduXs3hZva2CgVRtmCMctKoWTI/cmSLwObD59VKfcXe00hK1sgZKtbr83dUDOqLJmQbVLhNq8yqZKvnzLbc63+kbWEdhPOnTMFo/PlSi4ACt5gGupCtmdCGTLdHsv3222/x66+/qqtA9g5LjIvMM9N169YhNtbYXZMrsl2/fr0yW9vvpBnVauTIkRlIefLkyU5AMqbzpk2bTAP4iR83YM3BdMcL274zY3WtqxTGl4/UUn9kjmCaw91JtXcXOUfE0T4YdpbiEvlyYcFLzhlLXpi0BQt3ns6gPjp7FFYPaA6awYIl165dQ2RkpNcz9WC1x6x6eE/w6tWryJ07t1lVmKqXxw+as+GMGTPAcbMXWrFo2SpY0HzTqZ6O0rxKrNlueiMv23sWpxKvoXqJvGhSLqPzZrV3/3IZorRqXB5MeKoBcmW/GV5UT93BLHP9+nVVHY/uMrPQKnf58mXlCxSuonfueyTb4cOHKwcpmnDtvZCZOJ67TSYloHAiGnV+62lny8QHNGtTXO1saX52FDpbkazNkhcnb8OiXWkZc9z4KqFT/eJ4u30lVYYfC08vVs0PljpdN1C6k5MRERVl68YthaIx4+lGTt3q8NUaHDjrHOFm+tMNUb5Q8AiBHwt+EL05sJk1LsHSS7IlQen1jg9Wu/TWwwWR9j4yZzUXDvYyZswYlUozf/78elWaWo4fZmLtKs63Y8UtPvsHZy8nOc2nQfdUxn/qxZnazkCVJyUlKX+MrEC2DAmsl7ACxdWM5/Pm1ReXwCPZfvnll7p2hSRbOi4ZIa7I1tWZLTMSMUFCqM9sZ2w6hhcnbkgn24yRmDQ8fn/2dtQvk/ax8mZGLjfgj5vpR9IVuCLxhxuUwrBOdTJAzsTunb5egY284pDuMMW9LHe2W99tF9SdrZiRjZgNoddhVTMyFwneZPmeM3jih1VIunHzSKV2qfyY/PRtGZJmeNMTit/FQSoUqJtbp0eyJZlx1V62bFlzW5HuVcvVHE3W3I0ybCQnlGa+fvLJJ5XJ2oreyAt3nMLsrceRcDlJmbN4XrrzxAXE5cuFh+qVRKNyN01wnsiWd2cZRo4EqRl8Sd/01aCHs72MfaoxWlVJ2+VTGFKO9w4Pnb1s+5sW//iVu6vKma1JbzAd+7gYLFTIfUAFk6oOitpwJlsCxIXqjuOJ2Bt/EU3KF0JRh9sBQQHRj0qEbP0AzeKPeCRbhm5kSr2ffvrJ9G7s3r0b99xzT4Z6eK2HxEvZt2+fumfLq0EUOm/xWpI3M0uwrv7oBUgjW+5Chy/YDe6MmaKuTun8WHcwAVdvJKcnl03ziyqRPxozXmiGSWsO267+dKhbAs0qFlZh40Yt2oudJxNVqEWGb3TMosf7gvmis+GbpfuwL/4SyheJQe8W5fFAXc/5avX2x1052dkGiqA1ng812WpRoo4nXFUr0EsXL6JSiUJoW6N4hjNXZrhasSfNV6FZpSJg6r1wFiHbcB491233SLYffvghVq1a5dXjN5iwcLdNByNPTkb27bEq2Y5dcQCDZjABdZqk7UK1/3fT81gLTuGIMTOP3DlsMUjaGcTB5vx0ywr4ZuledR1JE/pJzevXEhWLunfUCnRMhWwDRdAaz/tKtrToTFx9CAfPXELluFh0vbUsmCnHH+Hd9XafL1XxiR2PUhg28c+Xmqu7sr+vP4qXJ2+0pcujI+Dnj9RFBwNS3fnTbiOeEbI1AkVr6fBIttu3b1dBI+bMmYMKFSpYq+U6W2NVss0QBcoWnCLj9Z4IpKJllaL4sXtjp95OXndEJcN2FMeP0qONy6iPn6O8/2BN9SE0S4RszUI2uHp9IVuSY2uHBWDBmBxY8sodfl2x6ffrRkxdf9RtIo0Bd1fFM60q4M5PFmNvfFqEO02YhYdkHK4iZBuuI+e+3R7Jlt69NOOWLl3a5X1aXguwusu2VcmWiQRssVdTU9ODWGS8mkPi/KlnEzSvVNgvsmUUqXtrFccHf+4QsjVp7sqZ7U1gx/y9H4NnbXdC2j6qky/DcPuQv3A04Ypbsv1P/VJ478GaqPXOnAyWG9aRN1c2bAlCDGNf+uNLWSFbX9AKj7IBeSN//vnnQrY+jrN2Zvv98v14b2bah8ltCrxUYGH/lqhYxNnc686M/Gq7KsrrmCY8kvS++Iu4+/OlYkb2cZz0FheyvYnUG1O3qMQXjmIf1EUvrizXatgiHDh92evOtvn/FuGwnWMgn2X0tOnP3+5LdZYqK2RrqeEwpDG6sv4YUlOIlFh1Z2vvIHUq8Squ3nA4e00n4bUD27gNEWfvIFWuUAyebHoLOjcu7YT09I1HxUHKpPdPyPYmsHwf+4xf54T0jOeboXYp3/NefzJvF4Yv3K2c/uTM1qQXOMRqs3TyeHvstSD37sZDz8XyEI8lrEq2jri0+ngRDpy5eW2Hv9cokQ9/vGh+hhEzxkjObM1ANfg6fTmzZete+mUDpm88phpKR7wezcpj4L3V/Gr4tRspePy7lVh14Jwy/0RFReD2cvnwf43LiTeyX4ha7yEh2/QxefbZZzF//ny3I2RkIgKzXoNwIVtmDBo0cxtW7j2DCESgRZXCePPe6qalwDMLb02vkK3ZCAdHv69ky1bxvjkzUxmVwpHJPk4kXkWlonlxIeGMutOsJ6hFcBAypxYxI5uDayi1ejQjL1myBMeOpa1S7YVntTVr1sRXX33l9Z5rKDvHusOFbEONk9H1C9kajWho9PlDtma2ND4+XsjWTICDrFt2tl4A/+2331Qs5NWrVwvZ+vhyegvX6KM6yxYXsrXs0PjUMCFbn+AyrLDsbA2D0jKK/HKQYqL3Nm3agFlCqlXz7zwmWAjIzjZYSGesR8g2NLgbXauQrdGI6tMnZKsPp3Aq5TPZcts/YcIElbzdPguPVTstZBuakRGyDQ3uRtcqZGs0ovr0CdnqwymcSnkkW+aCZUIAe2GsZEqHDh3w6aefWr6vQrahGSIh29DgbnStQrZGI6pPn5CtPpzCqZRHsp05cyaYu9ZeGDGqWbNmqFKlSlj0U8g2NMMkZBsa3I2uVcjWaET16ROy1YdTOJXy2YwcTp1jW4VsQzNiQrahwd3oWoVsjUZUnz4hW304hVMpl2R75coV/O9//8Pff/+t8snef//96NGjh+U9j10BL2QbmtdRyDY0uBtdq5Ct0Yjq0ydkqw+ncCrlkmyZx5ZJ3Fu0aIHr169j5cqVKpfsgAEDwqlvqq1CtqEZMiHb0OBudK1CtkYjqk+fkK0+nMKplBPZ0gGqSZMmePvtt/H444+rvjB4BZ2hNmzYoDuPrFVAELINzUgI2YYGd6NrFbI1GlF9+oRs9eEUTqWcyFbLYbts2TLExcWpvhw/flztcqdPn47q1auHU/9kZxui0RKyDRHwBlcrZGswoDrVCdnqBCqMijmR7bp169C5c2esX78eefPmVV25du2aCs84btw43HbbbWHUPTEjh2qwhGxDhbyx9QrZGounXm1CtnqRCp9ybsn2oYcesjlEMZDF5MmT1e62ePHitt4NHDgQ0dHRlu6tmJFDMzxCtqHB3ehahWyNRlSfPiFbfTiFUyknst26dSvoIKVHaFbWdr96yoeijJBtKFAHhGxDg7vRtQrZGo2oPn1CtvpwCqdSmf6ebaNGjTBv3jzLjMmZM2kpwjK78GMRFRWFXLlyZequMnn8xYsXkT9//rDsJ1PV5cvnPrE7Y6B/9913HssEs+N04CTWmT3F3uXLabmtc+fOHUx4g14XraYJCQkoWLBg0Os2qsICBQroUpUlyFYXEkEqFBERgdTU1CDVJtUIAp4RKFy4sLrm507atm2rPoZWEs4fzqPMLlmhn5mhj2vWrNH1KmZ6stWFQhAL3XPPPZg2bVpYBgjxBaYvv/wSpUqVwoMPPujLY2FXdteuXWB+51GjRoVd28OxwY8++iiGDx+OIkWKhGPzdbd5/PjxalHerVs33c+EY0GmHP3vf/+Ln3/+ORyb71ObhWx9givwwkK2gWNoJQ1CtsEdDSHb4OJtdm1CtmYjnIX1C9lmrsEXsg3ueArZBhdvs2sTsjUb4SysX8g2cw2+kG1wx1PINrh4m12bkK3ZCGdh/fxYMDhI9uzZMzUKY8aMQYkSJdC+fftM3c+9e/di9OjRKnGHiPkI9O7dGx999FGm9+j/9ddf1ZntI488Yj6oIawhPj4eb731Fr7++usQtiI4VcuZbXBwlloEAUFAEBAEsjACQrZZePCl64KAICAICALBQUDINjg4Sy2CgCAgCAgCWRgBIdssPPjSdUFAEBAEBIHgICBkGxycpRZBQBAQBASBLIyAkG0WHnzpuiAgCAgCgkBwEBCyDQ7OUosgIAgIAoJAFkZAyDYLD750XRAQBAQBQSA4CAjZBgdnqUUQEAQEAUEgCyMgZJuFB1+6LggIAoKAIBAcBIRsg4Oz1CIICAKCgCCQhREQss3Cgy9dFwQEAUFAEAgOAkK2wcFZahEEBAFBQBDIwggI2WbhwZeuCwKCgCAgCAQHASHb4OAstQgCgoAgIAhkYQSEbLPw4EvXBQFBQBAQBIKDgJBtcHCWWgQBQUAQEASyMAJCtll48KXrgoAgIAgIAsFBQMg2ODgbVktSUhJWrlyJM2fOoG3btoiJiTFMdzAVrVmzBvnz50elSpUMrzY+Ph558uRBdHS04bpFYeZFYNu2bfj333/RuHFjlC5dOiw7um/fPpw6dQq33npryNov88819EK2IXslfa/4xo0buOOOOxSRlC1bFm+99RZKlizpuyIPTyxatAibN2/GSy+9ZKheR2V9+vRBnTp18Oyzz+qu5+zZs2jSpIlT+XHjxuG2227DwYMH0bNnTxw4cECV6dSpE959911kz57dbR3z58932YatW7ciZ86caN++Pfbs2ZPh+RdffBEvvPCC7nZLQesj0L9/fyxbtgyNGjXCQw89hDvvvNPQRgdrXv3www/466+/MH78eEPbT2Xe5oo/88/wRlpYoZCthQfHsWmrV69G7969sW7dOkRFRZnSck7SP//8ExMnTjRFv6bUH7Llbp4r9jFjxqBMmTK29hUrVkztYrt3764WIkOHDsXx48fRsWNHRbYPPPCA277MmzcPr776KqZNm5ahDBczERERimw7dOiAe+65x/Z7vnz5UKBAAVPxEeXBQ+DSpUuoW7cuZs2ahSpVqphScbDmlZFkSyvahg0b1E6f4m2u+DP/TAHbokqFbC06MI7NOnr0KDp37owTJ06gVq1a6n99+/ZV5Lt7925VvGbNmnjzzTdRtWpV9d/Hjh3DkCFDsGrVKuTIkUOZnd9++21cuXIFn376KWbMmIGCBQvi0UcfVbvAkydP4pFHHgF3kNRPmTBhAnLlyuURpbVr1+KTTz7Bjh07UKpUKTzxxBNKH3eEJDuavStWrKh2y3fffbfSFQjZzp07F+XLl8/QpvPnz6Nhw4aYNGkS6tevr35j3STdr7/+2iPZ0kJAjFwJyZYfEfZHJHMiwPef73D16tXVIva3335TCzDudDkX+O7SmsF3werzygiyvXDhgsKA86ZGjRr4/vvvbWTrbq74O/8y5xvluldCtmEy2iTIzz77DAsWLFAEmjdvXpQoUQJTpkxR5EKT57fffou9e/di+vTpuH79Ou69915w181wfhYAACAASURBVNerVy+kpKSoyUMyIiFv374dr7zyitq9cQI9//zziow//vhjRY4kKkqDBg087qJpOmrTpo0io4cffhj79+/H+vXrFanz75ysJCuS2fDhw1Xb+FGzJ1vuWLlwcCW5c+fG6NGj1U/azpYmPu4sK1eurHav3GmS2PkxXL58OYoWLarKjx07FlOnTlV1uhOu1p977jllOuSigmZE6smWLZt6hP/O3TI/uMT7/vvvVyZ8kcyDAHe0/fr1wzfffKN8ILiT49EE369ChQops+ywYcNAPwO+j1aeV45kS/M4F9Gu5IMPPshgIeLC9KefflI4cOHKI5lWrVrZ5r+nueLv/Ms8b5H3ngjZesfIMiV+/fVX/PLLL/j9999tbSIJb9q0CXSM2LJli1qRcqdL0nnyySfVOUu5cuUylK9duzbeeecd2w5w8uTJakKOGjVKnfX4Ykb+4osv1O6XBE3i1oS7ApLs0qVLUbx4cRtxtWjRAq+//noGsr169apqrysh6bVs2VL9dPHiRbWD5gJCW30XKVJE4cEzVu7KuUMh+VKI1ciRI9UOhRjxY6HJfffdh2rVqqnz6dmzZytnLVoPaD7v2rWrwofCBUJkZCRSU1PVQoeLC5K3EK5lpkXADeEClRYXmky5sKIkJycrZykuSulw9Pnnn6v3LDEx0dLzypFsOa84v1wJFxVctHNhzgU4F6Y8cnnqqafUItlRPM0VLrA9zb+ABykTKBCyDaNBdCRbkiqJITY2Vq3Gr127poiAfyeBcuW6cePGDD0kKbdr107tLu3NwyQwEouvZMuVM4Urf3th/fybvXl24MCBiiRZj/3OlpOdHzVXQqLj4sCVaH1hXfxIche6YsUKkIAp9jtbtoNWAE26dOmizukchbreeOMNZRLXdrdaGbaTu2qaybnqF8kcCDiSLRd1tAbxHaB1Ji4uTllX+G5wbll5XjmSLecV31tXwvNp+jqQjOmoyEUp+825weMgb2I/V+iU6Gn+edOVFX4Xsg2jUXYk2w8//FCR1I8//qhMPSRWmnP5QaDpi4T2zz//oHDhwrZeamcrdAhytXqlGWnmzJnK3KxH6Iy0ePFitTu0l4ULF+Lpp59WpjfuGilc+ZLkuWu0J1vuHB577DGX1XHlbb+Tty/Ej2K9evXUAoG7VMcz20GDBqkzbk9nto6Vcifeo0cPZSVwdVZNszU9wsUbWc/bER5lHMlW87q1t5LwihrJhWe4Vp5XjmRL69Lhw4ddDgQXEPa+D9zJ83nON81XwdWCVFNmP1e40Ddi/oXHG+NfK4Vs/cMtJE85ki13iCQ1ntXyWtCIESNsZmR+FFq3bq3OGHkmyesvnEgvv/wyHn/8cVWeTlIkYk4yflhoPuI/uWujyZS7Sp6N2puHHTvOnSR3ejzjffDBB5VT1t9//63qZf0kUX6c6En9zDPPqPMgkpU/DlK8PsFVeNOmTdWuk+3nbnXJkiXKdEyzOXf5vngjc3HBFT6dy7gQ4dkddZPAaTImvvRE5tkdzevcydNszrNdkcyBgCPZau80F53c1fJMl+83yZZe8FaeV0Y4SHGBynnB//HYh98Ziqe5wt/9mX+Z4w3S1wshW304WaIUJzvPFLWdHh0auHvUTLCcGFxtat7JPK957bXX1O6OwpUnn+d/0ymKO1JNaEYi0ZCESYTUQ+E5jbfgEPRW/Oijj2y6SO50eCI5UievVlC0v/Pf2W7esyUB6xV6IQ8YMMCmj57UdBoj+VJoVuZCQVvJcxc6ePBg5YntTugQxgWAJlzJk8QZ1IBkSzO9hh/L0MTMRYlI5kFAO47QzmzpTEjvY75vFB4dcNFFfwi+s1aeVzw6YVuNuGdLyxF9MWhKp3iaK/7Ov8zzFnnviZCtd4wsX4KOPdyB0lPSldCLl97KmvOHVoa7xISEBLW7dTyf5C6PJEXypbOIK+GOV3NGYpnTp0+rdtiTG//ORQF3ht5IWw/QbA/rofCc2dWum+TIvjr2151+4kBTNk3Wjvdn6RhFKwEXDPRGdsRJT5ulTHgiwPeM1h0u6jL7vNI7Qp7miqbD1/mnt+5wLydkG+4jaHL76aV45MgRl7XQNE0TtoggIAj4hoDMK9/wygylhWwzwyhKHwQBQUAQEAQsjYCQraWHRxonCAgCgoAgkBkQELLNDKMofRAEBAFBQBCwNAJOZMvDbQZG6Natm82hhU4i9E5lCio6xDCij55Lz1boOUMZMrqJVYTpp7SgC1ZpkxntoCcj7/4a4RRlRvuM0kmHLQbqyKyJCeiJy+tV2l1po3DzVw+d/Yg1HZcys2ge/OGaQlPv2NDz+9y5c8qBMrOLE9kyowwD3tPlWwOAQQh4t9BetPuSVgeIl9G1qzBWaCvDItKLNrMLCYhk685DOrP0n2RLz+3M+rFgZLI5c+a49cgN9jhysUqsswLZcpOj16M+2ONgVH0kWy6gssIGxCvZMgwXA9TzbiGztvAaBGPbksAY3svTHUajBiQQPUK2gaDn/7NCtv5jZ6UnhWxDMxrc2QrZhgZ7s2r1SrZa6DL7IN2MGcoIQYyoQzKzsgjZhmZ0hGxDg7vRtQrZGo2oPn1CtvpwCqdSXsmWmSAYqsw+oD1Noc2aNQuLsHVCtqF5HYVsQ4O70bUK2RqNqD59Qrb6cAqnUm7JlnkM6dzCkHUMB7hr1y5btB4tfRvj51o91ZiQbWheRyHb0OBudK1CtkYjqk+fkK0+nMKplBPZMii9ljjcviPMnKKF5mPcUKYsY8BuOsFYWYRsQzM6Qraecb+enIKlu+KxL/4SyheJQasqRZEt8mY+YG+jtufURazYexrZoyJRLS4We+IvIuFyEhrfUhC1S6Xl8zVChGyNQNF3HUK2vmNm9Sf8ume7c+dOlX7M6rtagi9kG5pXUMjWPe7XbqSgw4i/sevkBVuhqnF5Mf35ZsiZzfuVlomrD+GNqVuQmgqkgv8vAhF2PP38HRXRv10VQwZeyNYQGH1WImTrM2SWf8AvsrV8r+waKGQbmtESsk3DnYT4957T2HE8ESXzR6NllSJY9O8pvDBxg9PAjHi0HjrUKaH+npIKLLd77s5qxZArexoRNxv6F46cu5KmH4Djfjh7VAS2v9ce/GegImQbKIL+PS9k6x9uVn5KyDbIoyP3bIMMuMnVebtn233sGvz17ylbK4rkzYmH6pXEN0v3ObXspTsroV/byurvXb9bpUhak2KxufDnS82RK3sUar0zR5GxRub2u1qt/IKXW6JikTwB917INmAI/VIgZOsXbJZ+yGey5ceFSYIpPMe1+qVr2dmG5v2TnS2w/Xgi7vlimdMA3F+nBGZsOub0d21nu+FwAh4audzp9wF3V8UzrSrIzlaCWoRmUptQa5YOauENz+vXr6NGjRqq2Nq1a21OU96eC9XvQrahQV7IFopQX3RhLm5fMw574y+5PbOdvO4IXpm8yWng/lO/FD75vzqQM1uJIBWaWW18rUK2XjDl7pYSDom0hWyNnyB6NArZut/Zcofao/ktbr2Rve1sib94I3t3JNPznlq1jJiRrToy/rfLZzOy/1WF5kkh29DgLmSbhrurM9s5fVugUEwOjwPj7szW23NGj7ac2RqNqD59Qrb6cAqnUm7Jlh/L48ePIy4uDrGxsRn6xEAXo0aNwqBBgyyf1UXINjSvo5BtGu6uvJHz5MzmdVA8eSN7fdjAAkK2BoLpgyohWx/ACpOiLsn2559/VkSqSZcuXfDqq69CS/fElHWPPPKInNn6McjijewHaBZ+xJs3soWbrqtpQra6YDK8kJCt4ZCGXKET2SYlJaFRo0YqGMQDDzygYiIzv2316tXx448/qryWQrb+j5uQrf/YWfFJIdvgjoqk2Asu3mbXlqUdpBiGsWvXrip9Hk3IlDVr1qBXr14oX748xo8fD0aQkp2tf6+hkK1/uBn9FMMl7j55Efmis6NUgWi/1eshW4ZRPHj2EioUyQM9JmS/G2PCg7KzNQFUHSplZ6sDpDAr4rSz/eWXXzBkyJAMWX7Ypz179uCxxx5T136efvpp9e9y9cf30Ray9R0zo5+YvvEY3pq2BYlX07zqa5bMhx+ebAQGnPBVPJFtckoq/vvrRrA+CkMf925RAa+1r+prNSErL2QbGuiFbEODu5m1OpHtkiVL0LNnTyxduhTFixfPUDfz2D766KPq7yRfo8mWH67Tp0+DpoVixYq5THJAMxIDaTAjkR4RByk9KBlfxqoOUjdSUlHvvXm4kE60Ws+fur0c3umQdn/cF/FEtu7u2c56oZki+HAQIdvQjJKQbWhwN7NWJ7JNTExEgwYN0KdPH/Tv39+pbmb6eeKJJ9TfjSTbCRMm4J133rHVRxM2PZ5r1aql/kYPaC4CDhw4oP67U6dOKjtR9uzZPeIjZGvm6+Net1XJltlx2nyyxKnhTW4piEl9bvMZLE9k++7Mbfhhedr7ai8fd6qDTg1K+VxXKB4Qsg0F6oCQbWhwN7NWl97IJ06cULvKIkWKuKx79erVOHbsGO655x7kyOH5vqDextMJi85XdM7iB6xv376gsxbPiCndu3dXO9qhQ4eqK0kdO3ZUZEsnLk8iZKt3BIwtZ1Wyjb9wDY0+WODU2bbVi+Hbbg19BsET2X42fxe+WLjbSefYpxqjVRXXc8vnBpj8gJCtyQC7US9kGxrczazVskEtSLY0Jw8fPhznz59Hw4YNMWnSJNSvX1/hQaIl6TI+s5Ctma+If7qtSrbsTbcxq7F0d3yGjg1/tB4Ys9hX8US2zMzTethi0BlLk4IxObDklTuQN5f3u7a+tsWM8kK2ZqDqXaeQrXeMwq2EE9ny40FTsh4pUKAAIlylHNHzsJsy06ZNw4IFC5THM4m2WrVq6ny4ffv2WL58OYoWLaqeHDt2LKZOnaquJWmyd+9eJ6133303eNZsFTlz5gwKFSpkleaY1o7Lly8jMjJS5T22mly8dgMTVx/G2oMJyJ87O9pVL4bWVfXtNC9ev4FFO+IRly8XGpUrgOTkZFy8eDFDjPDL15NV7OMS+XPh9IVrmLT2CA6dvYxKxfKiS+PSKB2A97MZWGphV3lEw/7YC300Zs2ahYIFC5pRtc86z507pyxgRn93fG6IyQ9cuXIFqampyJ07t8k1hVY9+5iQkABySbiK3rDFTmS7bt06dO7cWVe/jTyz1SocNmwY2AZ67X700Udo0qSJy3u99JoeOXKkuqKkCc+ZHeWvv/7CypUrdfUnGIW4mNE7OMFoj1l18KPNDyIJN7PIkPn7MXnjSVt3mOj9hy7VUaFQLtuYfrPiCMb8cxR0xKK0qFAAwx6sjCi6IltQOD7ah44+GrRI2Avv2U+cONEyCUc4f3jEldnJllY9SmaaP65ef5ItvxXh/E3Uu3lyIlstYAWB6datG6pWdX9NgeelRp3ZOg4EnaMYRIP3frWdLZ2ztHNkVztbV4MpZ7ah+cJb2YzsDyJXb6Sg6puznR6tVjwPfupaU1krDp65jJYfL3IqE04OUY6NFzOyP29L4M+IGTlwDK2mwYlsudIgqfEslDtCmm8Z0ELzCg5WB+bMmYMXXnhBmYD54jme2TKcJB255Mw2WCPiWz2ZjWwX7jyFHj+scQIhd44oLHupkSJbd1d9/L1W5Bvi5pQWsjUHV29ahWy9IRR+v3t0kNqyZQu+/fZbzJ49G7fffjueeeYZZdY1Q0aMGIHmzZurnTTv2vbr10+d92neyExYz4QI4o1sBvrG68xsZHvk7GU0+5/zrrVw3pyY+3Q9RbaLd8bjyR9WO4H50p2V0K9tZeNBDoJGIdsggOyiCiHb0OBuZq26vJEXLVqE3r17q3YwSQEnoNEyYMAA/P777za19Drm+W3p0qXV3/bt26fu2R4+fFj9N6/+DB482KsZW8zIRo+UPn2ZjWzZ63rvzse5K9czAPD4rWXQt3kJRbbXbqQo7+OjCVdsZXhUO7dvS1QqlkcfcBYrJWQbmgERsg0N7mbW6pFs6RE8evRozJw5U5Eed7b3338/cub0Paydnk5cv35dOUbxPq077zSajvk7/6dHhGz1oGR8mXAnW/o37Tt9UQFTvnAeFWrxROJVvD5lM7YcTUR0jijcVr4wXru7ElKvXbJ5mJ9MvIpx/xzE9uOJKJU/Gp0alkbtUuERLcrVWyBka/zc0KNRyFYPSuFVxiXZ0gORZ6ELFy5ElSpV8Nxzz6Ft27Zh6TEmZBuaFzKcyXb9oQS8MGG9bYdaMn80vurawEaab07bip9WHrQB27FOUXz6aKPQAG1yrUK2JgPsRr2QbWhwN7NWJ7Il0TIUIoXeyK1bt3ZbP89vre6yLWRr5uvjXnc4k+2DI5dj4+GEDJ3Twjn+s+8MHv3G+SrZTz2boFnFwqEB28RahWxNBNeDaiHb0OBuZq2Wu2drdGeFbI1GVJ++cCVbZuqpNPBPpF+TtXWWEZ+2DGqHMX/vx+BZ251AePXuqni2VQV94IRRKSHb0AyWkG1ocDezViey5bkpoxzpEWbmsfqlayFbPSNpfJlwJVsiUWvQXKesQOULx+Cv/q0wed0RvDJ5kxNg7z9YE11vLWs8kCHWKGQbmgEQsg0N7mbW6tZBinGHaVJmVh3ecWWItHAUIdvQjFo4k+2Q2f/i6yUZQ38+3TItD+2ZS9fR8n+LwJCPmsTkiMLSAa1RKMaYpByhGTHXtQrZhmY0hGxDg7uZtbokW4Y4tA99GBMTo2IR161b18y2mKJbyNYUWL0qDWeyZajFKeuPYNmutGQFzSsXwX/ql0K29JCL+05fwoRVB1X841sKRePeqvnRoFJ4pMzzOnAOBYRsfUXMmPJCtsbgaCUtTmTLtHbNmjVDmTJlMHDgQJXmjhl2rl27BkZ1YlzScBIh29CMlpFky/PTGRuPYtHOU7h+IwVNKxbGI41K48r1ZIxfeRAbDp1T/854uXlyZkOT8gXRpXFZ5MpuflxmT1l/QoO8sbUK2RqLp15tQrZ6kQqfck5ky8wfvOYzZcoU1K5dW/VEi5e8ePFilCxZMnx6B0DINjTDZSTZjlq8F/+b82+GjnRpUgY7jiVig4PXcGoqwERU99Uuji+7pKVjNFOEbM1E11l3fHy8utNsdV+RQFERsg0UQes97/bqDxPEa4EltHyyEyZMUMndw0mEbEMzWkaSLaMy0XRrL7lzZsNlu3NT7TfG9lbZhiKA3R/cY3q2HSHb4L5fQrbBxdvs2pjdiA65WoIZs+sLpX63V3/++OMPW5QmmpLbtGmDTz/9FA0aNLC1Ny4uzvIrTCHb0LxeRpJt5YGzMyRgZ4+YwM5V0rpUpCIi/ZcFL7dExSL6Io35i5KQrb/I+feckK1/uFn1KSHbEOazNfqlELI1GlF9+owk225jVmPp7jRnJU0qx+XB0bNXcOl6xmTnmhmZUZ+Wv+Y+IIu+XngvJWTrHSMjSwjZGofm1aQU7D51AXGxuVAkr38heBkPfPfJCyiUJyeK58vlc+OyNNmePXtWpdjTI3fddZfXRAB69JhZRsjWTHTd6zaSbHccv4BnflqLA2cuqwr5YeB57MEzlzBoxjZcTidcEi33vAVjcuDTR+rhjipFTO+8kK3pEGeoQMjWGLzHrjiAj/7coZJnUJpWKITRjzcEg7folYmrD6kAL9r8a1C2AH54shFio7PrVYEsTba6UQqTgkK2oRkoI8lWUWgqcODMJSQlp6BCkTy2s1j7lTV/u3QtWWXY0a7pmN17IVuzEc6oX8g2cLzjL15D048WIilZrU5t8sY91dC7RXldFSReSUKD9+c76fA1naSQrS64w6OQkG1oxslosg1NL7zXKmTrHSMjSwjZBo6mu/jevnjwu9PRtnoxfNutoe5GCtnqhsr6BYVsQzNG/pDtnlMXMXvrcew/cwml8udG+5rFUa14XnAVvXhXPE6ev4qapfLhtvKFQtMpF7UK2QZ3KIRsA8d727FE3Dt8mZMiXqf78KFayvNfC9pSoUgMbimcR91lT7ichEblCuCxW8uqdJNtPlnipIPBXz75vzq6Gylkqxsq6xcUsg3NGPlKtuP+OYC3Z2yDurpj52fcq0V5/LrmMM5fSbJ15N7axTEyCHdo9SAnZKsHJePKCNkGjiWTbbT7fCm4uLWX35+9HWUL5c4QjtSV13+LSkUwrkdjPDRyudM997FPNUYrH3wlhGwDH0/LaBCyDc1Q+Eq2jd5fgFMXrqmAFPaSLTISSclp0aHsZeHLrcBVd6hFyDa4IyBkawzejPE9bsUBbDl6HnH5cuGheiXRqFxBp0Qb7q7YrRnYBjmyRdoiuBWOyYkOdUv4nGZSyDZ9PJcvX47ExES0b9/emBEOgRYh2xCADsAXsqWZuPa785QTlCPZsvWuJvzoxxugXY240HTOrlYh2+AOgZCtuXg7JuGwv7duX/PE3rcacpwjZJuO6osvvoiLFy/i+++/N3eETdQuZGsiuB5U+0K2VCM729CMk7daJTayN4TM+T1U4RodHZ9ckS2vB619sy1yZgs89riQbfr7M2LECEydOhXMAhQM4S6BK9eCBQsiZ07Xl6z5e548eRAdHa2rSUK2umAyvJCvZOvqzJY72jql82HPyYs379ICuL1iYTzWpAyOnL2MynGxaF6pcNCu+jgCJTtbw18djwplZ2s+3m9O24qfVh5MqygVKJAnB85duq7+MzZXNgx+sBYeqFvCkIYI2abDePr0aRWm8YsvvkDLli0NAdedktGjR2PYsGG2n2m6fu+992x5dA8ePIiePXuCiRIonTp1UtmImG/XkwjZmjpsbpX7SrZURIeNqRuO4PvlB3D5WnpkKHVUm4qieXMhJTUVZy6mTXo6UtHmzJ/rls6PKc80NT0OsqvOCtkG9/0Ssg0O3olXb+DA6UsoVzhGEeyRc1eUkyLvsOeICnxHq/VCyDYdib59+4Ixkt3J2rVrkS9fPkNGf9KkSSqtH3PmHjp0CN26dUPv3r3Ro0cPpb979+5qRzt06FAwsX3Hjh0V2T7wwANCtoaMgLFK/CFbtuCz+bvwxcLdGRpDUxZSI5zOc+3PeH/s3hgtK5sfMcoRJSFbY98bb9qEbL0hFF6/C9mmj9f8+fMV8bmTrl27ujX3Bjrkb7zxBg4fPozx48dDyzpEQq5fPy1tGomWpPv1118L2QYKtgnPeyNbxmWdsPogVu07i9w5osDL8LxX++QPq7EkPWm7fbPcOU9pXlVv3VcdPZrdYkJPPKsUsg0u5EK2wcXb7NqEbM1G2It+Zhlq3bo1OnTogFdffRV79uxRHtH0ji5atKh6euzYseo8efr06UK2IR4vV9Xbk+315FSMXrJXXYxnqMUX7qyEN37fjFmbj2d49P0Ha2LDoQRMWX/ESaUrj2RlSmb2n4gIyM7WnJdAHKTMwdWTVoYg/WjWVsz/Nx7nr9xQgSQGtK+GqnF5PTZm/+lLKt7xkt2ncSM5LeZxzZL58PJdlcG7sVaULE22zC24fft2NGzYEKdOnVJXONxJtWrVEBUVZfgYDhw4UJmv586di2LFitmS19ubrX/55ReMHDkSy5bdjIRC72lHmT17NlatWmV4G/1VyIWEt3Nmf3Vb6bnk9LuxDFHRaviaDNl5IiMi1JlrxsisQM3iedDn9tJ44bcdGbqiJRhwvGur5a7lcz88VjMkZ7ZsA/uaLZv+AO5WGicmYc+fP79q0uuvvw56wdoL587EiRNtZULdds4fYu34LoS6XUbW/8PKoxixNKNF8ZZC0ZjSo67Hap78eSs2HbngdNwSkyMKM/vUR/5o672jnD+0DoXzN5EOvXrEKZ8tPY/79OkDmpCHDBmChQsXutVj5JmtVgk9oIcPH44pU6agdu3a6s/azpbZiLQkw652tjt2ZPxI89n7779fLR6sIsyqpHdwrNJmf9px+fJllet44oaT+PDPnU4q3F0pWD+wNZbvPYOxKw5h89EE9VFtWDY/nri1LE5fvIaF/8Yr4s4XnQ1lCuRG9RKxaFaxUMi8kUm0vB5nlO+CP1gH8gzx1RYKu3btUgsHe3niiScwa9YsFChQIJBqDHs2ISFBYZ1ZyTb+wjX0+mkDGFLRUVa82tJtKjzOifrvL0SyQwQ2Tcd3j9dHy8qFDRsHoxSRbHlMqC34jNIbTD16FwpOZEsy2LZtm9rZ8nzE0862atWqhu1saU6g8xPPZX/++WfUqFHDhperM9tBgwbhxIkTcmYbzLfKh7o0M/LLv+/A7K0nnJ7MFhWBGw5ZR3wJhO5DU0wtKme2psLrpDyzntleuHoDfcavxYq9Z9wGd2HUJnd5Z/l8nXfnuiVbX8MoBmtUs7QZWS/IdJwqUaKEYeYzmrB+++03jBkzBuXL30zzFBcXp+p48sknERsbK97IegcoxOVItglXkzF29XGMWbbPqTXZs0UiKT2XJn/klYJvHm+IWwqHPgSjL9AJ2fqCVuBlMyvZfrN0Hz78M80y58oZsGLRPFjwX8/XLzt+tQLrDpxzMiPnyZkNywa0RoHc+vPMBj5S+jQI2brBiTvMefPmKVJcv349jDQj0yGK3seOQnN2uXLlsG/fPnXPVivDqz+DBw/2mrxe7tnqe+mNLMVA5z1+WIXFu7lKT3Ntsg/DyD+p89bICHVpvlzh3FjU/w7wP8NNhGyDO2KZlWyfn7A+o8Ng2m035M4ehVvLFxQHqeC+ZqbU5mRGdqzl+vXrygmJXr90NqKQ/B5++GF191Wvvdqo1tN0zPu2/J8eEbLVg5KxZSavO4JXJm+yrdJV5AnNnVjzioogBd8UrrxLF9AXFczY1gamTcg2MPx8fTqzku27M7fhh+VpAXvs5Y8Xm6NGiVhfYQqb8ll+Z8tdx6ZNmzBz5kzlqEQPxZiYGPVPOi+FU2ICIdvgzrujCVfw2HersD8+LX2XljDPMcGAo4OUkG1wx0lvbXL1Ry9SgZVbfygBHUctz6CkfOHcmP/fViHxsg+s1eU3jAAAIABJREFUN/qfztJka2+uJcHee++9yqOXpNWkSRNMnjxZRXkKFxGyDe5IPfG9c1AKV2dQ9n/jedS8fi3FjBzcodJVm5CtLpgMKbTmwFlM3XAUJ85fRdWiudG5YQmUKWoNL3BDOuhCSZYm23Xr1qFz586oWLEiPv/8c1SpUkVBpHkEC9kG9tqdPHlS3R3OjMKz2koD/0SKwwVaR7LVznFzZY9C0wr6zqOsipeYkYM7MpnVjOyIoresP0t3x+PzBbux41giShaIRudGZdCzefAjqAU6+lmabPkyf/bZZ2oHS+Euls5I3NW2a9dOdrYBvl1ZkWyZiuuq5nmcTsQ0KzNiVNdbywaIaGgfF7INLv5CtsC5y0loPvQvXLx2IwP43z3REG2qhddCPkuTrTZ6V65cUan1pk2bhsWLF9sGleETu3Tpos5ww0HEjBzcUXJlRr6vdgnM2nwsQ0PoeczzqApFwuM9coeikG1w3y8hW2DxzngVQ9xRnrq9HN7pcDM+QXBHxr/ahGwdcOMLPmfOHHXlR4vGxGw7H3zwgWmJCPwbOuenhGyNQlKfHjpI8b7g8t3xyB4VidbViuH19tWwaOcpfLdsH/bFX0L5IjHo3aI8HqhbUp9SC5cSsg3u4IQD2TIB+9Yj51EsXy60qlwEsdGu77f+ezwRP6w4gDMXk9C+Zhz+0+DmfPBkRhayDe47Z1RtXq/+OFbEkG70Uv7111/VnVurh6kTsvX+qjBX5bLd8UhKTsGt5QuhcrGbAc+ZY3bF3tOKOJtVLIzSBXN7VwioyGOMm507t77yupRasJCQbXAHxepk23fSRkzbcNQGSr7o7OD1nVIO19omrz+M/pM2Z7h/3rBsAfz2TFP1rCeyFTNycN85o2rzSrZ0Ztm/f79KZ1ehQgUwohMTuefMmVP9u9VFyNbzCC3aGY/e49YgyS504nsP1EC328ph3D8H8M6MbSqiDSUqMgJfdW2Au6p7PxcSsrX6zNDXPvFG1ocTSx0+d0WdpTrKM60qYMDdVTP8uemQv3As4UqGv/E63I737kHuHJEeyZYPiYOU/nGxSkmPZMsA67169VKRoijDhg1TydqfffZZRcBakAurdMZVO4RsPY8OQ7ytP3hOFdJIleeptUvnx/74S0i8mpRBQe2S+TDjhWa4npyCSWsOY8We08iRLRJ3VCmK++uWtF3fEbK18qzQ3zYhW/1YuTPvMr3duB6NMyiq9MafSHJ02wcw5qlGuLNKUa9kq79V1i4pZ7bp48M0dvRMZiL3H3/8EcwAQrJl2i0mjv/7778tf41FyNbzZKs1aC4YxFwj2gxhFUnAKUBk5E0d3N3u/fAevDF1CyasypgG7NW7q+LZVhVUYSFba3/k9LZOyFYvUsHd2epvlbVLCtmmj899992nokU999xzKjQjiZb/Y2YgXgWyT4Nn1SEVstW3s3WVnJ1PpqSmgvlnNSEp//1aa9zzxVJF0vZSrXhezH6phZCtVSeDH+0SsvUNtGCc2frWImuXFrJNHx8SLe/Y0pRsT7ZaftlFixahVKlSlh5NIVvPw6Od2V6/kWpz1lBBJ1Q84wgVoCIigkEX08MbR0Sg/12VMWzerrQ/UNLjHOfNlQ1bBrUTsrX0jPCtcUK2vuHF0mZ7I/veIus+IWSbPjbMGbt06VJMmDBBmZK5q23bti369euHjRs3gsnc6XFqZRGy9T469Eb+768bsXr/2XRzMok3IsO/p+1yobySk1NSMihNM0Gnqms+PzzZSMjWO+RhU0LINjRD5S2CVGhaZXytQrbpmNJcTIJlph1K6dKllQmZL8LXX3+NO++803j0DdaYGcj28NnLeG3qFvBeXr6c2fF/jUvj6ZYVcDLxKsb9cxDbjyeiVP5odGpYGrVL5fMLwes3UtBs6F84deGa7XlXpuV0XnXKmVk8Xy58/2Rj0JRMkTNbv4bBcg8J2YZmSIRsQ4O7mbV6vfrDSFJ0lNqyZYv6gN5yyy0qvV7lypXNbJdhujMD2VZ/aw4uJyVnwOTFOythyrojYBAJTehFPLdvS5WI3R+xT42n9qrKhJxRE03MqakRGZymWOLrrg1wd82bV8GEbP0ZAes9I2QbmjERsg0N7mbW6pVszaz8/9u7EvCarq69kkgkiCFiHuLXmNVUY8yhhqixv+IrivjUVEp9NbSKUjVTU42tzzzU1NY8xTwTFCWaElVTDCGRqeF73h3numNy78095557stbzeKruOXt4917n3XvttddSomxXJ9t91x5Q6I+nTaDK5+tND58nmPz7wOBAik34h3ZevkfP45OpavE89J8WZahy0dzpwr3r8j36eMVZvZ2tlCDvzavY2b56mXq+C1MzxNPDjY6NbEL5cmTVPchkmy7cLvEAk61zhonJ1jm4y1mrCdnu27ePoqIMr3RYagBiJCO4hZrF1cl20o6rtOBgpAnECO6fKAX3f/0rdp3ZsnpSfJKhl3CR3D504D+NyMtD7w6PmUGDd3HDqQfocVyS+NWSGdnLw00XBAPtGBlSjnoElTAokclWzVphfduYbK3HCk8mJL+ksOsP6FZ0HJUumJMals5nkjry4l8xwj8idzZP8Xs+X9NvKJOtbbi7wtMmZDto0CCrg1Ug2AWHa7RtmG3N+vPHg1gKnhFGbsIf+I28E5Cbzt56avBvuKbz5rnXVCk8id1EyLhHcYkGabm61CxOofUM03IhCs7KE7fo+r1nlN/Xmw5HRNPfMS9SnaXETvYV9WsYKN679yyBSuX3JW9PUxJnsrVtXqj1aSZb60cGi1VciYMOSVKteG7a1L+u7v+n7bpGcw/c0P0/Fqvr+9YxsTwx2VqPu6s8yWZkhUfKVrJF84asCxdJpSXJnjUL7Rpcnzaev0Nz9kXQP68j0Xh7eVBCkuHZbipJEq3+d236ePkZk7Rc/+1VU6yuLQnK3njuLzp8/aF4pH7pfPR+taKUBQfEaQiTrcITS6bqmGytB3bVySj6YvMlkxfW9qlDtUv60YukFKo8bpdBaFQ83LpyYZrTparBe0y21uPuKk9aRbYwTz59mrqLypMnj6x9Q10pKSmUJUsWs/UgEHmOHDnIx8fHqna4uhlZ6uSzhH9o/9X7VMI/O1Up9ub8FQqMZAFIIB3y3WHhoWwseXN40bi2FWjgqvMmv8mVlovJ1qrpqfqHmGyJIqPjRFhSSL1S+ehZfLJZM7C5qGp4R8rbfPnvZ9Rq9mGTMdcPBiP9yGSretWwuYFpki1Ib86cObRs2TJx3QeCPLZ9+vSh0NBQWc5rt27dKmIwHz5sOCmR/KB379508+ZN0Y6OHTvSuHHjyNPTfPoqCQmtkK01I9t+/jE6H5Ua51hf5n5YlTzd3Q2cn6TfmWytQdbyM5z1J2P42fq20ll/Np27Q59tCH8TzpTcKAUxTF+5Ebm/oqweHjTvw2oiOQfvbG0dTSK+Z/sas+XLl9P48eOpfv36Ijyjl5eXIEH86dSpE02YMMF2dC28ATLt2bMn3b59W2QTMiZbRLDCjnby5MkiAxEiW4FscQ84LclMZLvs2E0a+/NlAzgK5/KhQ8MbU0x8MjWccsBmM7K9A8w7W3uRU9d7mX1n22R6GP3xMM4kwIsUyEXyyK9YJBfN/KAK9Vp2is9sbZjCTLavwQLJ5suXjzZt2mQA39SpU2nRokUiG5CjHKSwQ4iOjqa9e/fSwoULDcg2JiaGqlevTuvWraNq1aqJtoBoQboIrsFkm4oAMvHM3htBP1/4mx7FJppc+zFOy2XOQcoGPUnzUSZbRyHp3HK0SLanbz4WPhD3YhLo7SK56L3KhenXC3/TpTsxVDCXN7WvWoRqlPCjuKQUenvMThE5Tf/OuV6UUoPB6V4ngEaFlGdvZBumLJPta7CwewwKCqJhw4YZwCfFRkYS+bJlDfM02oCz2Ue3bdtGkyZNMiBbqb6jR49S/vz5xXswbW/evJlgdmayzSjqjn+fydbxmDqjRK2R7bmop9Rh/lEDKBGCNOmfFN29cfwID2J4Er/Z2aaGMIUg76zx7QD8O3wptgx443mckfHiM9uMoKfOd9M8s128eDGtX79eXAXSd1hCXGScmZ49e5Zy5szp0J6ZI9tz584Js7X+ThpRrebNm2dAyrt37zZpCzIWIfqVWuTZs2cOx0zqG1bftx6/oOSUl1TSP7vwerzxMJYK+GbV3eW7G5Mg7tEG5s9BuHYglyQkJJC7u7s4etCyYGX+4sULccThquLt7S2aHhYWRklJqXesJRk9erRY1Pr5+amie1jEAWuJ+Gxt1MSd12n5idsmrxlHS+teuxiNalGatl64RyO2XBbZr3QEay60GhE1KZuP5nWuZGuTzD6fmJgaNlXtcQwy2lk4xCJvuq9vaphXVxRJf9Jre5pkO3v2bOEgBROuvhcyEsdjt4mkBBAooqPOb9Pa2SLxAczaEHM72ylTppj0FwsGkLRaBOEvrfWktqXNfzx8QZ9uvEJRT1K9kbN5eQiyBfFCqhb1pZRXRBfvPNf9PvzdktSuUgFbqrH62eTkZPFBtORVbnVBKn8QZIu+uupHEQsi6UM3d+5csXDQF6TR3LBhg8OOizI6nFjEAWt7ybbf2st07E9TJ0LjAC5B/5eHvu9cQTT35uN42hR+j/578s31O3N8O6ltGWpZ3vI1Olv6jmM1EFF6DqC2lKnGZ9FHLCysJSw19sHao9Q0yRbKd+HChXT7B7KF45IjxBzZmjuzRUYiJEjgM9tU1P+9/AztuXLfYAgMzF1mwkFl9/KgU1++S/ivo4XNyI5G1DnlacWMjGhrEfef087L92nu/ggdmCKdpF76SIRNg7V4VEg56tOgpAHoiPo0e38ERdyPJR9PDyru50NZPDzIL7sntaxYiJqUSz3icoSwGdkRKKqrjDTJFmSGVUdAQIDsrcakxw4BJmtc/UHYSKy6pZ1Rjx49hPmVvZHND0X1CXsoOtbQBJj6IXETHw8Lli8RWapCYcceBaCFTLayq4wiFWiBbNefuS289HEnHXqAvMuxiakhTc3pBRJ5bOpXVzznLGGydRby8tWbJtkidCNS6q1cuVK+FrwuOSIigkJCQgzqwbUeEC8kMjJS3LPF1SAInLdwLSm9M0G1Xf3ZfvYG3YlzpwK5vKlBqXzCA/Lq3WeE+MVNyhUwG/rQGvBbfneIrt5NNRFLor+ZBfGaM70dHh5MxfJYFyDEmnZIzzDZ2oKWep91dbKFR3HNCXuEZ7G+9AwqQVfvPaMTkY9NwK9Xyp9WhtZy6qAw2ToVflkqT5NsJ06cSCdPnkzX41eWllkoFLttOEhY65CiJNkitCFiCSOucIB/dgoum98g+P+n68Jpi17YRQ93N0IeWTd3N3J7RZTD25OOjQimXD6WV9TIbXvkRrQ4iw16y184OkHmh/1BU3b+ngbZmqbLq1osN212kPek8XAx2SqpFfLV5epkaylqExa6tx7H0a1HhmfUQBK5mY+PdG6ubiZb+ea0s0pOk2yvXLkigkbs3LmT3nrrLWe1MUP1KkW2KS9f0fvfH6Pw22+SAxT3y0Z7hjYUXr8ITl5/8n6TvhjvOH19slD46GYEIjaW3VfuU7+VZwl1QWAeHtemAnWvU0LcBfw5/A4duPZAEHjlYrnpeUKy2O1KdwdxbvVL+N8UHZd6B7db7QDK5ZN2BC57wWeytRc5db3n6mRrSe/eq1SICuX2oUWHIo1SfBB1rR0gQiw6U5hsnYm+PHWnSbYILgEzbrFixczep0VwC4RvVLMoRbYHrz+kj344ZQLFtI6V6f/fKUph1x5Sjx9Nfzc+M8L//9izhtgVG0v7eUfpvB6Z43fkkD39ZVPVDQGTreqGxK4GuTrZotPm9GZZz5pUqWgu6jD/GN2MjtWZfRBjfEv/umbT3tkFoJ0vMdnaCZyKX8uQN/KsWbOYbF8PrjkzLn7q2/AtGtGyrOWdbWpSHgMZGFyKhjUrbTJt3h67i5DGy1gujmlGOWXaodo7d5ls7UVOXe9pgWwRqnTFiVsibrh/9qzUukphqhforwMad9PDo54SQi6+lU8dmwcmW3XpgSNaY1XWH0dU5Kwy1LKzRf+Nz2yFMfj1VQMJH97ZOmum2FcvJyKwDzfpLfg5zNpz3SDE6GfNyxD8CfTl6Ytk+nbHVdp35Z64Lx4U6C+u58CxUIvCZKu9UWWyddCYpndmK1Wj742M5CGD1xmmvYNzxpHhwTaf2TqoGw4rhne2DoPSqQXJvbNdcyqKRm4yjPDml92LToxqYuBciDyxyKqjL8jDjHzMWhQmW+2NaroRpBAq0ZIg6IW1XsHOgk6pnS36l543Mp4xTh4Pb8jFRyLp3tMEkSsTwczTystuyRvZWfhaqpfJVm0jYl975CbbgavP0a8X75o0zvj+d91J++nO03iD56AnEd+EmF2Y2tdb9bzFZKuesXBUS9Ik2yVLltDFixdN6kLgicDAQEIot2zZsjmqLbKUoyTZWtMBY7K15h1XfIbJ1hVHzbTNTLbOGUcmW+fgLmetdpmRES8ZqfAQoBxRntQsTLbOGR0mW+fg7uha5SZbNiObHzEmW0fPZOeXZxfZXr9+nVq1akW7du2ikiUN44c6v0uGLVCSbCMfxtG5qCfUoHQ+yu+b1SwUvLNV2wzJWHvYQSqD+LGDlFkAmWwzNq/U+LZdZHv8+HHq3r07k+3rEUXM1cbTwuj+s9SMO/AorlnSjzZ8XMdkzJls1agG9reJydZ+7Ox58+HDh5Q3b17VW9Ts6Zv+O0y2GUVQfe+nSbbLly+ny5cv61qNaEfIwLN//36qUqWKSL2ldlFiZzti4yVae9rQUxLXepZ0q07vVjBMYcdkq/YZY1v7mGxtwyujTzPZZhRBdb2PFJWPHj3SpU5VV+sc25o0yRbRo06fPm1QIzLvNGrUiJo2bUoFCsiTC9WRXVSCbJvPOkTX7hkmAUAfugeVoK/bpObElITJ1pGj6/yymGyVHQMmW2Xxlrs2Jlu5EVawfCXI9oOFJ+jUn49MejW0WWkaFFyKyVbB8Va6KiZbZRFnslUWb7lry/RkGx8fT1OmTKEjR46IfLJt2rSh0NDQdNPZyT0w9pSvBNkevh5NXZeeMEhh5+7mRqe+aEr+ObyYbO0ZOBd5h8lW2YFislU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   "source": [
    "fig = px.scatter(GA, x='pm25aqs', y='pm25pa', \n",
    "                 facet_col=rh_cat, facet_col_wrap=2,\n",
    "                 facet_row_spacing=0.15,\n",
    "                 labels={'pm25aqs':'AQS PM2.5', 'pm25pa':'PurpleAir PM2.5'},\n",
    "                 width=550, height=350)\n",
    "\n",
    "fig.update_layout(margin=dict(t=30))\n",
    "fig.show()"
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  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "These four plots show a linear relationship between the two sources of air quality measurements. And the slopes appear to be similar, which means that a multiple linear model may fit well. It's difficult to see from these plots if the relative humidity affects the intercept much. \n",
    "\n",
    "We also want to examine the pairwise scatterplots between the three features. When two explanatory features are highly correlated, their coefficients in the model may be unstable.  While linear relationships between three or more features may not show up in pairwise plots, it's still a good idea to check:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
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j2rRpUxF2QzvbSpUqmQ1aSldksk1pxLk/JQTSI9kGPnuNf84+RHjUWxHq079eETg7SFWn6EjyWNArkFRHw5K50LBEougM2cJDtzF9x3XZj78uPg72djj4ZSMU8FKXNjOzrjA1ZDuBUuqdkEaQLP64Gm4/fyNCfuj+tE35vKjlm0P8/5BVZ8VndEU+rnUpDGqoPwRILdmOWHMOm849lkxTzaLZsWZQbcWpi3mbIOKsyStdn2VIsiWpxB49eoBS3PXu3Rtt2rRBgQIFkpIBMNlm1q86P7clCKQnsj19NwSf/XUGzyJiZI9MIggLelUVXsgbzz3EyDUXJGX+6FMdjUvlxt7rz9B/2SlFyJZ8XF04Q114EIr8ni5oV9oL9coWtgTeTFFXDdnSnfr8A7fhfzUYnq5O+Kh2Yey49AQbzz2SYLRucG2MWX8Rd14kiltojIi5Wek8iniqJduLD8PQZf5RkLMWGW2a1w6qjepFssva/XTlGey8nHjH7OXmhEW9qyqWy5Bke+HCBXTt2lU8PMWytm/fXugTa1ScmGwzxfeaH9LKCKQnsq323R6Qt6s51rpcXszvVRX6YnN1HaHUEIg548iIdQxhdTjwBfosO4W38Qlil/pD1wp4v1qiRoHSPW6fOkVAiQp0bXgzP4zUo0SllmypzRevY/DXifsizKh7dR/k83SR9bXi+D18vemy5O853Z1x+qtmsrIZkmzpKUk4YseOHSKlHf139uzZ0bx5c/H/TLYZ8WvMz2RrBNIL2UZEx6H85H/NhqNu8Zz4a0BN/OofiF/8b8raCZreVpJYgMlWPdT6sKIQG0qnR8Smbf98VhdVfLwUybZ37SJYfkxOtnS87GifBbFvE9CmQj58XLtIUpOmkK2ap9KX//jW922EbrO2ZViy1TwkTd7Fixexbds2QbK0uyVFpy5duoiUd76+vmowTdUyfGebqvBz5/8hkF7Ilo4hiyuIUaidyIltS+OT+r4Yve4i1p9JVHvT2Ac1fDBdR6mIyVYtshAZfygZQI4cyXG1VHvz+UcYvvq8rCGN01nX+Udx+p40o9XP71fEzaevseDgbYMDILELiqkmszbZ/rznJmbvlWdkuzO9jUzjIcOTrfYskLoT5ZMlxymNqpS1FaTULzv1JZls1WPFJW2HQHohW0JA347DEDp0h0skS042ZEpHl6S/Szq82sZkq4wqOQw5OdhJFLr0YXXq7it0W3BM1tCXLUvi88bF8TwiBsNXn8PR2y/F/ekXzUtiSJPiovzWC49xPThC7CSJkI/ceiFpx9PVERcmtbAJ2QaHRaP5LwdBO3ONDWrgi/EKalaZimy1Z4Dershj+b333hPJAtKyMdmm5dnJPGNLT2RLs0Jexlcfh+PPY3dlusW6szatUzn0rFFY/JCTJvLKY/fw/U55dp/BDYslkbGmDSZbKZpn7oWAnIY0zmk9qhfCjC6JGtGGsOo87yjO3k/evZJn98ExjSXHsU/Do5HV2QHuzol61hqS1Yha9Ft2CvuuP5MMyN3FAZcnt7QJ2VKjdLe78vh94bFeIo872pZXFkvJFGR7/PhxrF+/Hvfu3cNnn32Gxo0bixAgOsqgxABp3Zhs0/oMZY7xpRbZ/nP2EfZcewpnezu0q5gPTUvngdofLoq//GbzFZkClPaMkaQrXTdRnGZ+Lxc8/C+dntKsruhfE/X9cvLO1sCSrzHNX+YF/lPXiuhWraBBsiUt6jn7buHVm1h4ujoISUzy7iWjne+AP08jLCox2UMd3xx4HBadlGavTD4P/D2wFvZee4pRa6Xe5dqynNY+Rjblm692zZrSZkqXNSjXePnyZXTq1EmEAdHDTpkyBR06dMDKlSvFf1+6dIl3tik9Y9xfukQgNchWydtzce9qqFnITZXOLP1A+197ahW85/asgrYKEo+8s02GV1+mpKFN/fBF8xIGydbQJNWevhdPwqINzmO/ekXxzXtloFuWTisOjG6EwjmyWv3O1pSFleHJdsKECSKl09y5c9G/f39BtPQPpbtr2bKluLstXjzx7D+tGu9s0+rMZK5xpQbZVvr2X9kRMBHejHZ+esmWhCy2X3widqu/KjivmDtrSh6m1BaTbTKi+jIlkbbwtE7lUTZvVkUHKaU5IT3q569jxIkDhWEZs8qFvPBH3xqgNaNrGkcr3tkaQ9Hw5wZ3thRfO3r0aHTr1g39+vVLIlvSRqbPKO9tmTJlLBuBjWsz2doYYG5eFQKpQbalvt6F6Lh4yfialsqD/3UpqUi2FKtJAvLWNorpnNy+rGKzTLZSWMZuuIg1p6Re3FQiq7M9zkxsijcR4TJvZF1gP156EgdvPjdpGslTnOQya36/l8nWJOTUFzZItn369EHOnDlFEndtsiWSJRLmRATqgeaSmRuB1CDbaduvYVFAkAR4Cr15r7S3Itk2//kgaGdrzCgnraujPY4FvTRWVBxN0hGlPmOylSMzau150F27rs3/sDJq5Hc2SLahkXGKu1Pttijbj6NdFpBMosYo7vbbDmXR4Mf9klSK9PnGz+uCdr68szW63A0WMEi2u3fvxpAhQ9CrVy+Qo1STJk2EwMWMGTOEuhQ5SqV1451tWp+hzDG+1CBbOgqeuu0qVhy/L8JIhjctjoENiik6SH3211kh62fMqJ1SeT0Q8zYeN4Ij9BYf1qQ4OlQuiGK5shpskslWDs+8A7fw467ExC/atvijKqic18kg2ZLecetfA2R1a/lmR42iOYS6VPtK+fEoJBq9l0pPMUhxisK3SF+ZnKq8szrh524VhfwmWWqQLTnpzdx9EwduPEXubE7oW6+YRH/b2HpNS58bzWe7evVqQa4kaKGxdu3aYdKkSfD0NJ5w2JSHpS8eTSgRurOzs2JV+tzd3V11xiEmW1NmgMvaCoHUIFt9z6LrbBIbn4ASE3da7dEr+3hh42d1VbXHZCuHiRylqn3nj8jY5CuAPB4uOPxlQ4SHS0UtqAy9AGkUl0iUxG/CDlnyhzk9K4vctRr7Ydd1oaGsa3dntNU7b6lBtkP/PidigbWNdJ2VdJZVLbhULGSUbGlsJGhBso2RkZEoWLAgvL29rT7k33//XRxXa4wUqr799lt4eXmJP1HoEYUa3b2bKDFG98jkEe3oqD9TBJVjsrX6VHGDZiBga7Il55rotwnI6pSclYd+iEl6z9GecvIkGiX2jo2OhLOjA9zc3JL+VnbSbjOeCmhVLi/Co+KQz9NVhJJU8fHGqBYlxDGzGmOyVUbpyuMwLDwUhEuPwlG1sLcQpyjo6ZTkIEUxtXQaQcIQZB0qFcCvPRKzsQ1Ydgr+WvGybcrnw7wPq0g6Uso5SwWU1Js0FW1JtqQ0+Sg0CrmyOcPZIXm9KomjEBYk2JHeTBXZpsRDke6yj4+PSN93//59kXFo4MCBwguajO6MaUdLR9dPnjwRx9iaUCRD42OyTYnZ4z6MIWBLstU+dqSjv9EtSmDp4bu4/Tzx/rVDpfziePDTlWfxICRS/M3J3g45szmDhA7aV8yPE3de4XFolLHHkHxOYSF3puvfCalpjMlWDUqJZbSxqvfDfjz8by41LUztWA4ujvb4cp00VpZ2gbQb1LZ1px/gy/UXFTuvVtgbUzqUQ9n8HpLPbUW2h2+9wEdLTkAj7dyxUgH8778XhwxNtvPmzQNl/lFjP//8M7JmNXwno6YdpTIUdkS76RUrViSl9yNCrlIl8Q2NiJZId8GCBQa7YLI1dwa4njURsBXZ0g9Vr8XGPYhJNeh1TLIsnu6zebs5IiQyUfRArdEd349dE9WNzDUmW/XIabDy8s6OYgr61SRAQdKHf5+U5rOlHpR2rNN3XsfCg7cV8w3Tejj7dQuhCqYxW5AtnciQFrc0hQLwa4/K4iVRyZeA8uJSftz0ZrKd7fz581WT7axZs2xCtnFxccIZi+6Gx4wZg1u3bonEB6TNnDt34mX9smXLhE4zeUZr7OlTeQB+vXr1EBgoF7tObxPF47U9AgkJyd6Z1u4tJCQEHh4ewgvYmvbr3ltWjYc1ZWw3praUHFGbUldTNj4+HuHh4Ta5mlIzHju75CNLNeU1ZWy5VnTHcTzoJYatviCkDSlu9pv3SmPy1quy4dIONnc2Z2xXcHQL+r613sejeGpaR7q2sn8N1CmWnPSAQj7pWs9czJQGEPg0Ai1/PSz7aHhTP+HQR2T8/Y7r2HD2IQp6u2J0i5JoVDKXKVNltbKWPneaOUbWRmTixInYvn07yBs6T548IsSoe/fu0E58QI5bJLYREJDseffhhx/KgD158iSTrdWWW8ZtiDx3afdpKyNSsTbR0lhXnQnGLwfkOxlbPYem3V7V8mJ4Qx+LuyHchdyjmaRn6QBy5TL9h9vWa0X7mSg/bb3ZZwTpmGsNintjVgc/vdUXH3uE34/KQ42oQoX87hjXrAj8crnBFms4PPotms49KxvbwDoF8EntAkl/p5cbkgalf1LLzFkr2mM1Srb0NkNKUeSgREZp9WiXaW1PZM2g5syZg9mzZ2PDhg2oUCHxiEqzsz169Cg0D6y0s1WaBD5GTq2lyf1qI2CrY2T6MW7/2xFcfRKe1F2Notlx8s4rq05Abg8X1CueAwW93VAiTza8pyC9aE6HfIxsGDVKDEAJAkwxcqhydbLHs/AYNCudG2N0Mi1RW6ShTCpTxOGkV/3BouMih62SUVKDI+Oa2Cz0p88fJ3HgRrIIR15PF+z/opF4Bo1leLlG8vylpPG6Rve0ixcvRrVq1UxZAwbL0psLOT/Rvexff/2FsmWTFWcoyxD1pX1nO3nyZAQHB/OdrdVmgBuyJQK2IlsaM4V7/HHkDl5Hv0Xp/B5oVTaviJM8cuslKE5RKWeoqc9K3sXXprYytZrR8ky2+iGiuesy7yjOPQg1iqN2gQ9r+ohUhrQLzOaSmOFH2249e432vx2WhBaRdy/ltz108zlCImNldY6OawLHuNcixtcWpxArjiXLS5IzHylmaVuGJ1vyAKZjWiK5cuXKCZApmTw5JxHR0U7TWkdj48ePF9mFlixZIklKT0kQHBwcQGpWdOfF3sgmfe+4cBpBwJZka+gR9entmgoLZZA5/438xdvUdnTLM9nqR3DZkbuYvPWKYgHKGzzr35uIizfsZ0ChWCsH1ISb1i5x0pYr+PNoYgilxormzIr9oxvhf/6B+J+/XEv51MRmQHSiVKQtyNbYOsrwZFu/fn00a9ZMCFhom0ZZiv5Nx8rWMHKIIu9jXaO8uUWKFBHJDyjOVlOGQn+mTp0KJ6fENFL6jI+RrTE73IalCKQ02ZIm8rwDt8Xx3MWHpu2MlJ6VtI1J49jaxmSrH1FKIKAvGQQ5Lq36pBYo/+2A5acR8iZxN0oOVLQj1jZKt/f1e8ka9n3/OIn9Wse2mrIBYxsjPDIObedIHZYqFPTCliF1bXaMrGZNZXiyHTZsmCAzbbEJAoYIj8jR398fhQsXVoOV1crQjpribekfNcZkqwYlLmNrBFKabNv9dhiXHoaZ9VgkKkDkSmFF0XEJaFkmD96vXsistoxVYrLVj9Dm848xfPU5vQWGN/NDizJ5RTysJjF85W//RVy8lGxJy3rT58mKXm1+DZDc8Wt30LFyAfSo7oNFAbdx+/kb1C+eE1+2KgkPF0cmW2OL2cjnBh2kdu3ahaFDh2Lp0qUSPU46WqYQIbpbpXsBUnEiUkuLxmSbFmcl840pJcmWdrLkNGWulc7ngZ3D65tb3aR6TLaG4VKSK9St8deAmqhbPKf4c5f5R8VuV9u6Vi2Imd0qij+RMlXb2fJQG+3yy/rWUAyvsUWcrdrFkuF3toMHD8bevfKUS7oA0b2qdgiOWgBTohyTbUqgzH0YQyAlyTYgMFGRx1xrUTYvFn5U1dzqJtVjslWGa/XJ+9h+KRgO9lmQO5sL1pzSH96luW+llsgLvfvC4yKcioxOKTZ8WgeUE5dMTRpF8gYmeUe679U2JluTlrassMGdLXkjkyewMaOj5tKlSxsrliqfM9mmCuzmLbQrAAAgAElEQVTcqQ4CtiZbEj44evulUPxpXDI3Os41f2dbzy8nVvavmSJzyGQrh5mcl8iJSdvaVsgH/6tPJWnxNJ9T5OkdrQQCJLu59vQDcX/bs6YPcronJ3UhhznSwdbNc6w7ChLHODmxGY4HvcLR2y/Eumrg44rKxQuwg5SZ3wyDZEuxrPQjQblr06sx2abXmctY47Yl2e66HIzBK88kAUY/jDo+MiaDeXNaa6GfbGtjspUjXHXqHrz8z+FJ82mTUrmxsFdljFl3Dv9ceCapRPe2C3sbPomg+/ef99zE8/AYUfd17FvhVEU7X+28ttoN/9K9EkauOZ/0JyLvTZ/VRoVC1k9EY2ydZfhj5FGjRiE0NFTc2aZXY7JNrzOXscZtS7KtMc0fzyISf0TVGv1wFvB2xYNXiYkJdO3G1FZwVpm5R22fSuWYbOWoVJi8G6SspG2UYq9xyZyIi43F4TvhwiGKrEQed/zZrybyebronYZz90PRaZ70pKNk3mzYPaKBqDPz3xv4bZ9crpF2xCQRqW29avrgu07lLZlys+pmeLIlB6iffvpJyCRSrGt6NCbb9DhrGW/MtiDbsKg4LAoIUvyhNISgl5sjNg+ugcK5vURYkK4zVVUfb2z4rE6KTAKTrRxmEiGhXag+83BxwLZh9ZHV2QE5sspDH+k6YeelJyLxRNkCnoiIilMMITo5oSlIGYyyBzX7+ZDkaJmcqtafeSgbAgmmLEih+3ztzjM82ZJMYteuXUWau6ZNm8qAL1mypNVELWz1zWaytRWy3K4pCJBzibd3djg4WJ6IgDK7zN1/C/+ce4Rn/+1wTBnLgRG1kNvDNSmfLR0xzth5HTeCI0Re1EntyigqD5nSh9qyTLbKSBHhLjl8R4TxUDJ5XRvZvAQofpaO+il5vMaO3X4ppBe1jRLLk8qYrmnIlv7+MCRKOGFRf0VyuKFHDR98+tdZQdraNrZVSXzaqHjSn+hlj3bOOd2dQARNMbm2MFuQLTmRESz2dimjt2zwztaYN7J2YgBbAGyNNplsrYEit2EuApO3XMEyLbUeSnU3+4PKoDs4jZEK0OerzuHfK8HiT5Ts+7eelYWDi5K1/jUA17S0kE0ZW34vF+z+vIZ4SdYkjzelvrXLMtkaRlSNNnLLsnnw+0eJ0rlTtl7BH0ek6lD6erir5VSlVIZOTgb8eVpIf5K1Kp0T8z6qnuQgRXlz12ntfikM1H9UAxTLpU4DwZS1ZG2ynbDxEladSPTwpheFeR9WBWmK29Is8kYm/eK0frzMZGvL5cNtG0Jg1cn7mPDPJcUipDWb38tVfKYkn/d54+IgvVpdO3svBJ3nHzUbeBdHO5waU4/J1mwEU7Yi7TRLfLXDqMPbV21LY0B9X4z/55JiPlulUV+Y1AKero5GH4iSXdjZZcHLFy8kco1Kid2HNvHDFy1KGG3T1ALWJFt6QaAXBW3zcnXE+UktTB2WSeWNZv0xqbU0WJjJNg1OSiYZ0jebr2D5MeVdBuXlHNIk8Tiu3KTdssTulLuza9VCyOPhjA9q+OD8g1AhvUgi8tsuPjYbQW83JxwaWYvJ1mwEU74iHQ33+/MUomLj9Xb+cZ0imNK+rCBaIlxt0+edPqKZHxzs7IQgxt0Xr1G+oBeK59a/K9WOs6Uj2KLjd8jGM6RxcYxuWRLzD9xG9Nt4uDk6YFBDyyV9rUm2s/69gTkKDmGk/U0a4LYyg2RLd7aU2FmfUQo83tnaamq43fSOAN2DLjh4W/ExZr1fEV2qFBSfGZLPo8/9crsj8Nlrq8BBP3xD6hVksrUKminXyO4rwRi0Ijm8S1/PtKbIM3nugdtJwhamjLJ1ubyY30s5jEhX1OKDhcdxLOilpPnl/Wtgtn8gTmupWFFS+3WDa5syDFlZa5LtL/438at/oKwPW4e78Z2tRUuAKzMC+hG4HhyBtrMDZIm/y+X3xNah9YRQABnlFf1q02WbQ5nL3RnbhtWDW5Y4Jlubo23dDmLi4lHq611Qk0J+aodyeBQapfdFz9jI6Eg1Mi5eaCRPbl8myXdAl2zJUW/MhgvYeSnR18CQrfqkJuoUS5SUNMesSba3nkWgxS8BkoQNTUvnwZKPrZcyVukZDZLt48eP8ebNG1m9sWPHwsfHB7NmzWJvZHNWDtfJNAgEPX+DjecfISLiNVxcXeHu7IiBDX2TBCOeR8SgwU/7DR4RWgus3rUL49sO5WDNHy5Lx8YOUuoQHPfPRaw+Kc2KRhKMlx/JFf761i2CJ2HRILETS6179UL4oUsF0Yw+ucZf/APxq0JaPu2+SZuZvJXNNWuvWXIw3HYxMTyqgJcrBjaw/Kjb2LOZdWd78OBBke7u7NmzyJYtm7E+UvVzvrNNVfi58/8Q0BdnS7lDKYdoStiwpn4Y1bwEk21KgG3lPkp+tQsxb6V3tlULe8uSDlC3JNFInux0YmKpaUtB6iNbctgjxz1DdmhMY/hkdzN7ONYmW7MHYkFFs8j23r17Is/thg0bQPe2admYbNPy7GSeseknW+Vk3dZGpnS+bNjwaV2RRDwt/XDxztb4TIdGxqHG9/6IfStNFE96yeQ0ReFBtjJKhHDu6xYYuPx00v1sh0r58WuPyqLL289fo/eSk+LYWp993bY0+te3bOeYltasuVgbJNtnz54hKkoKIj30ihUrQInjjx07BlfXxPCFtGpMtml1ZjLXuPSR7aHAF+htQYYetSiWyeeB7cPqi3vitPTDxWRreAYpEXzTWQdx54X8Ok/t3GvKkXJY+4r5RcIK8mrXtaqFvXDmXqjkz0ObFMeVx+EyQv+iRUlUK+yNnouOK94jU7L6RiVyoVAON6tobKelNWsq7pryZjlIZc2aFSNGjECfPn3M7VdvPXIpj4+P1+vlTEcZlDheLckz2Vp9irhBMxAgst10LQxLj9wDKfp82qiYCOkhW37sHr7ZbHsHqd96VsF7FfIx2Zoxf6lVhULHKITMGrZuUG3M2nMTlCFKyfaOaogHIVH45+wjRETHiZy2FFKkFE9LHsaujvY4FPhc0hStbRJtIWEWNRYZG4+vNl3CpnOPQeFuUzqUFVmrdC3Dk+3169fx6lWieojGiGhtKWaxefNmzJw5U5Yfl46u6Z6Y0v6RdevWDVOmTBGJ6w0Zk62aJc9lbI3A7N2X8fN+6R3aj10r4v1qBaEmQbg1xke7DZL4S0s/XJltZ0s71dHrLmDj2UdCKGJQg2IY00ouXqKZ7zn7AjHrX/06yWrXBWkaU+pEJa93uped+2EVvQTpN3EnSOVM24hMLz8Ow/2X0kQWdHJyZ3pbtcPC+78fEzl4tW3VJ7VQp1gOyd/S0ppV/XA6BQ3ubGkXSbJu2bPbVsaKxkRk2rdvXzx48ABKyej79esndrQ//PADnjx5gs6dOwuy7dChA5OtubPP9VIMgarf/ouXkXGS/srm9xA/cD/tvmHVcZAqEN3vRcUlO9SQwwwF7Xu4OjLZWhVt0xr7Yt0FbNAR+J/YpjQ+0eMNS9l9ak3fK1GQIllETXJ47d6zuTiAwnHIKB9t41K5ERwWLZLAk3Pcr3uV/QP2jW4E35xZZQ9COXHJq/lRSGJ+XG1bOaAmNp97JJFrpM9blcuLBVpxum9i34o2Cmd3g6NOykZaoyW+2inrl46u6Zha2zIs2eruImvVqiV2m3ny5DFtZZlQmt5w6ajN398fv//+u2RnSwnsq1WrhjVr1qBKlSqiVSJaIt0FCxYw2ZqAMxe1DQIUQrDgwG28iowFxSmGRsWJf9MxHKVHqzr1X7x8IyVbW4yEBDB+7FYRcW8T8OX6C7j3MlKENlDoRe3/dgtp6Ycrs+1si47bLrvjJDL8x0CWJbqzJUckjRHZerk6IETr5a2BXy78/lFVrDn9QAjrU8iObj5iElghoRVdu/Fda6w7/UDsMMkhqkmpPFgcECRUy5SMdL2X9qku0jr2WnwcN58mjq1Enmz4s1+NpHR/2trJtONd0KsaSMdZYyRF6TdRrkKVqciWdotEuJ9//jni4uKwcOFCVK9eHYsWLbLF74Okze3bt2PGjBkSsiUlq9atW+PIkSPInTvxPJ8S22/cuBF07GzI+BjZ5lOW6TugXUab2YcVkwMQ0R78shEW77+OmfvUCcSbAygJVpz6qpmqqky2qmCySaFiE3bIRE7oeHdl/5qK/dH96ai1yQncNYXozp/uTCmbDwnp965dRO94KZEAJRSgxAK69k27MqB705kmnq5oh/IQ6dJ3gNa6xiipxkAdxSt6Sbg6pSVcnZIzX/VYeFx2h7x6YC3U8s0Ex8gkZNGwYUMsXrxY/Jts165dGDp0qPA+zpnTfBUQNatXiWwpnrd79+4ir66np6doZvXq1Zg7d66ElJcsWSLrgog7MDBl4hjVPB+XSbsIvH5tniSi/40XGLFOvxPLF0190b1iDmy+GoIdV57jeUQsHhoIlTAHIcomdPzLuqqqxsTEiMwtxvwdVDVmYaGEhATQeNQ6PFrYnaw6XU2ZakQsSmI/atqZvf8OFh5JzDajsVmdy6BlmVyK1evMPCJLJE8Fu1bOB1pXdHRszJrNOSGOk7XN09UBa/tXRQEvF1T8/pDsBcBYm7PfL4cmJaSEqF1n3qF7mHdI/nK5qGcF1Pb1TioaHRePmf5BOHonFLncnTCgTiHULy6/tkwLa9actaKNiezO9sKFCyKHrTaxvnz5EnSUvG7dOlSqVMnYPFj0uaGd7dGjR5ErV+KiVNrZEgHr2tdff81ka9GMZJ7K5v6ArjnzGN/u0O/E8lmDwuhbPY8gFHq733QhGBO3yI/zLEF6UP3CGNaoqKomYmNjxTjSCtlGR0enWro/cvg0x8xdK9TXn8cfgF7QXBzs0KVSPrQqK/e+1Yyp7NQDBofXpXI+fPuefgerd++Act8pt3H5q4ZiHZT77qDJOsqHR9WBt0Lies1gV5x8iBm7b8nGfmBkHUGqplpaWLPmrhXNs8rI9syZM+jRowfOnTsnHJLI6EHJA3n58uWoXdsyQWljICuRrdKd7eTJkxEcHMx3tsYA5c9tjgAdw1WZugf0lq5kAWMawzUhEt7e3sLhUOmIzdxBOjvYg+T5xrUupboJPkZWDZVZBSnZ+/Qd1xFw6wXye7qIEJqo2AThsFShYOLJnFqjRPCU9ceQLe9XAw1KKO+MqR5l51FyqNLks/181VlsvyhNEq8vUxC1p0Z6kfrrNO+o5N6XRDjm9kz0uTHV0tKaNXXsRsmWPIK1jYiNvJKdnJLfSnbs2GE1uUaaHLof3rlzp3DG2rt3rzjq0mQVopheDw8P9kY2d6a5nk0RoHsxyl1L2XnI65JCJfJ5uuKHLuXFD6FG1CIm/h32XHmK4Wvk93DmDLBe8Zwgz1BTLC39cGVEB6luC44lJVzXnZfBDYuZ9GJ09+UbfPLnaYNZn0Y0KwFKl6fPft5zA7P3SneZ2tl9xm64iDWnkr2NKRRo7xcN8Tg0Gi/exICcr+h++GzgA1QuXgBuzsZz4NJY6Dd9yZG7eB39VqTuoxhvcy0trVlzn0G2syXHKKW7T6UOxo8fb7W7FrpXbdOmjaQbctQi4iULCgoScbYUGkRGoT9Tp06VkL/SGNlBytylwfUsQYB+aOYfDMKFByGIjksQTiDxCe+EQ4s17aNahTG1YzmTmkxLP1wZjWxj3iagpEI4i/YEnf6qGXK6O5s0Z+FRcbjyKBQfLD4pq/dth7JJDlKTt17ByuP34WifBSOblUgS2N964TF2XH6CZ+ExqOeXCyP/I2c6jaFsQvpMOxuOkjbymXuvRH8Uc0svfiObl4CHizoyNgUAWrO0+bL0KNeUPq1d1ixtZGsPwpT2aIdNx9tqL6uZbE1Bl8vqQ+Duy0gMXXUWlx6FiZ0r/cBpFKC06/y2/xZWHLuHsKhYQbK2tGwujtj0eR0Uy2Wakw+Tre1mxRh5Uc90EkHEZKrRi8kHC4/h1P3kHOOUjGDDp3VEUxM2XsKqE1LnKzoOJk/1jpUK4MtWJWWxrucehKLT3CMGh/Jdx3LoVauwLOvPg1eRImMV3QtrjGLHSRbUmkZxuoOWn8LFR4nP3aVqQczqVtGaXaRIW+mObE1FhcnWVMS4vBICLf93CDeCIyQfUUxhQ627MhKnmLtf7hRiK0Q/rFkY0zqZtqulsTDZ2mpGEtvtPO8ozt7XnwXnwqQWIOERU01zCrAz8DVevI6Fq6MdBjUsltSMvrtZTYFavtmxemCyzw1l6um64Jgkr6vSmDTZonR3tpStirJW6VrA2MYo5G1+hh/d9pSO5Se2LY1PLExuYCr+lpZnsrUUQa6f4RGIjU9AiYlypZvhzUokHccRCEpp0GwJDsVajm2l3jFKMxYmW1vOCkBHviSLuPXiE3i4OEjiW7/vVF6kwDPHjB25+07YgQQj1xTXp7aCi2NinOvnf53F9ktSxyilcWnuhNWS7Z6RDeGXx7TTFkN4KGkzd6tWED91TV+7WyZbc1Y918lUCNDvl+/47bJn1nZMoTIkWKDk9WkJWLQD+uuTWggOixLCBBqjH/Ftw+qblSOUydaSGTG97ss3sbj+JByU7N3UHa3/tac4fTcE9lmyoGGJHCjmmQU5cijHt07ddg1LDgcZHOCVKS2R1TkxNrfZzwcVs/9oN5AjqxP2j24kZD51yZbua7vMPybpj642Lk1uYTpIBmoo7dj71SuKb94rY9V+bN0Yk62tEeb2MwQCX2+6jBVaybjpR5M0ZenHiKzL/KOKibzVPDwJ0tcokl2mpEOydf3r+YJSo5FdeRyGPVefwS4LhEOM5u9q+tAuw2RrKmKpU37dmYcgyUNtW9ijDFpU0h9PTce6Oy4Fg7yYdfPfUk7jncMbJDWnu6bpA0oA0LlKQdB9LN330vrTCGcoOUjtvfYMQ/4+h6jYt0KucUaX8kKL2Zr2y56bQtdZ29YNrg3KPJSejMk2Pc0WjzVVESAxdsoD6uRgh141CyOvZ6I8HaUZowTaukbydSQkr2vaMYz036QzSz8c9OO36fwjFPRyw+T2ZUCeoLYwJltboGr9NslLWDd2u0WpHFjYp5bRzsi/gDIG7bocLDzgKfxsRufyyO+VnH/81ZtYfLj4RJLMaH4vF/zZt6beI2AlsjU6ECsVWHnkFm48ixRhRy3K5kHVwumLaAkGJlsrLQZuJvMisOzIXVDIha6RZyYl3ta1bUPriSQFweExqFjIU+YhamskmWxtjbB12le6qyyfPxu2DkvenVqjJyJmSgpQroCHweZSk2zT0po1F3MmW3OR43qMwH8IhEbGovK3eyTZXEgYYOvQenhvzmEJTm5O9rg0uaXIzJJalpZ+uIw5/aQWRmmh34+XnsTBm9Lk7P1rFcDXHW0rmavv2ZlsLVsVTLaW4ce1GQGBwKGbz0USeE1mFZJQnNSuLHZdCcaI1efFcSAdK8/+oDJqFk3dIzAm2/SxaJ+/jhHqUZpUd41L5sJP7YphR+BrvHwdI7LnDGzgC8pVnBLGZGsZyky2luHHtRkBgcDDkEi0/OUQ3sQm6yOTXjHJ85E9e/4cObJnF9rIqW1Mtqk9A6b1n/DuHbIgC+Lj5aIWlQp5YdPn6rI9mdarvDSTrWUIMtlahh/XZgQEArP+vSkcUrSN9ht3ZrQVf9JoIzPZShcMHyOr/wJdevAK7eZKQ22o9vTO5RXVzNS3rK4kk606nPSVYrK1DD+uzQgIBKZsvYI/jsjzdwZNbyOO+ZhslRcKk636L9CWcw8xbI00FIhqG0tEoL4HwyWZbC1DksnWMvy4NiMgEFgUEIRp269J0KDQoOPjm/LO1sAaYbJV/wV6GRGFqtP2ySps/KwOKls5tlVpVEy26udKqSSTrWX4cW1GIAmBvn+cwv4bz8T/U2jP4o+ro1qRxAB/3tnyztbSrwq9mPxzMghjtwQmeb5PaFMKAxsk6yNb2oeh+ky2lqHLZGsZflybEZAgEBUbj9exb0WmFW1jsmWytfSrojkF8M6eA88jYpA9q2OKxmgz2Vo2g0y2luHHtRkBVQgw2TLZqlooBgql9pE7k61lM8hkaxl+XJsRUIUAky2TraqFwmSriEBaClczdx6ZbM1FjusxAiYgwGTLZGvCclEsyjtbe7i5WS9PrqXzYWp9JltTEePyjIAZCDDZMtmasWwkVZhsmWwtXUM2rX/mzBlUrVrVpn1w44yAMQToh9LBITGPaGpbfHw8smTJAjs7u9Qeisj/S+NJK9ikOiAGBpDaWMXFxcHRMTHdY0pbWlqz5j57ht/ZmgsM12MEGAFGgBFgBKyFAJOttZDkdhgBRoARYAQYAT0IMNny0mAEGAFGgBFgBGyMAJOtjQHm5hkBRoARYAQYASZbXgOMACPACDACjICNEWCytTHA3DwjwAgwAowAI8Bky2uAEWAEGAFGgBGwMQJMtjYGmJtnBBgBRoARYASYbHkNMAKMACPACDACNkaAydbGAHPzjAAjwAgwAoxAhifbsWPH4ocffkixmY6JiRF9OTtL85mm2AC0OgoPD4eHh0dqdC3pMyoqSsjxpZbUW6oDwANgBKyAQEJCAui7lDVrViu0ZnoTlHnH3d1dSH2mtEVHRwt5UScnp5Tu2mr9ZXiy9fPzQ2BgoNUAM9bQmzdvhN4rLcrUNBoD5Z/MnTt3ag5D9E2kT0Tr6uqa6mPhATAC6RUBTkTAiQjS9NplsmWyTdMLlAfHCKhEgMmWyVblUkmdYky2TLaps/K4V0bAuggw2TLZWndFWbk1JlsmWysvKW6OEUgVBJhsmWxTZeGp7ZTJlslW7VrhcoxAWkaAyZbJNi2vTzDZpn+yXX/mIa4/CYezoz26VCkA31yp63yWphc8Dy7DIqBNthvoOxEcAScHO3SuUgDFUuA7QQ6XOXLkEF7BKW3kCW1vz2Sb0rib1B+Tbfom2xk7r2PBwdtJc+7sYI89IxvAJ4ebSeuACzMC6R0BDdkuPf0Cc/ffSnocItw9IxuisI2/E0y2lq0gDv2xDD9ZbQ79kQNqSehPkXHbZQ0ObeKHL1qUsPLMcXOMQNpGQEO21WYex7t30rEObeqHL5rb9jvBZGvZ+mCytQw/JlsV+JlLtvSDUnS8nGw/a1QMY1qVUtEzF2EEMg4CRLahoaGoNvOE7KE+a1wcY1qWtOnDMtlaBi+TrWX4MdmqwM/6ZFscY1rZ9odFxWNxEUYgRREwRLafNiqGsTZ+AWWytWy6mWwtw4/JVgV+5pAt7Wr/PHoXk7dekfUwrKkfRtn4yEzFY3ERRiBFEdAcI1efeQIJOufIQ5sUxxctkl9A9157iosPw2BvlwX96hWFu7ODxWNlsrUMQiZby/BjslWBnzlk23X+UZy+FyJrPXtWJ+we2QC53FNfe1rFo3MRRsBqCGjIduuNCEzekvwS6k3fieH1kdvDRfT1+8HbmL7zelK/BbxcsXNEfXi4OFo0FiZbi+ADk61l+DHZqsDPVLL1v/YUA/48LWv5/WoFMa51aRDhsjECmQ0B7dCfvdee4cLDUFBKgN51iiDHf98J2vD6Ttguc6Aa0cwPI5pZ5kDFZGvZimOytQw/JlsV+JlKtvMO3MaPu5LfzDVdLO9fEw38cqrokYswAhkPATWiFnHxCfCbuFP28Na4emGytWxNMdlahh+TrQr8TCXbx6FRqDNjn6zlT+r7ivunfJ6Jx2VsjEBmQkCbbLdfeoIrj8LFnewHNX2QX+s70XjmAdx58UYCzZwPKqNdxfwWwcVkaxF8fIxsGXzy2hxnK8fEVLKlFnZdDsaQv8/ibbw0oJAcPfaMasiEa+2Fy+2leQQ0ZLv6Ygh+2n0jabxuTvbiO0F3s2RXHofj05VncP9VpPj/QQ2LYXxry0PlmGwtWyK8s7UMP97ZqsDPHLKlZsX90/jt0Infh67npYohcBFGIN0jkCRq8dNxhe+EXOgl5m0CHOyyiN2vNYzJ1jIUmWwtw4/JVgV+2mS7//ozHA16KRw7GpbIhbrFle9gH4ZEYsGB21h54r6sh88acZytCti5SAZDQG2cbcI74Jc9N3Dizivk93JFrmzOIHZuUCIX6lvg88Bka9mCSnNk++7dO8THx8PBwfK4MIKGtZHTjjbyoaAwDFpxRrJi/+hbHY1LSscYF/8ODX7cjydhUYqre+6HVdC2fD7LVj7XZgTSGQKanW3/1ddx/kGoZPTad7IDl5/Gv1efKj7d0j7V0aSUeb8JTLaWLZg0R7abN2/GzJkzERAQIHmy77//Hn/88Yfkb1WqVMGaNWsMIsBka94Xy5Jl9c/ZR1h96r64b32vQj50rZADjo6OaDv3BIJ0HDdalMmLhb2rSrpbdeI+Jmy8JBsC7YYpcH9Ik+KWDI/rMgLpEgEN2UbAFY1n7k8K72lVLi8W9Er8DsUnvEOxCTv0Ph+92NILrjnGZGsOasl10gzZ3rt3D3379sWDBw+QN29eGdlOmzYN9+/fx/jx45NG7+LiIsoaMibblCXbzecfY/jqc5IpGdG4CAY18EX1Hw7hdfRbyWfVimTH+sG1JX9bRspRWkH7mg/XDa6N6kWyW7biuTYjkE4R0JDtF1tu48CN55Kn2DGsHsrk9zRKthUKemLLkHpmIcBkaxZsSZXSDNnSQnrx4gX8/f3x+++/K5JtSEiI2PWaYky2KUu2fZedAt3LapunqwOOj2mAn/zvYOmRO5LPRivsVKPi4lH9O3+8jkkm5ryeLjg6rgnssljH2cOUNcRlGYG0gAD9Rr4KCUWNWfJEBMOb+WHkf6IVHy4+gSO3XigOWbucqc/EZGsqYtLyaYZsNcPavn07ZsyYoUi2u3btQu3ateHt7Y1mzZqhenXjxyFMtrYhW/IU3nD2IYLDotGlasGkUBwlsvVwccCJsQ3g7OKC0esu4p+zD0Gc2bOGD6Z1Kq+4gi8/CsP3O67hWNBLccc0oU0ZFMuV1bLVzrUZgXSMgFqyfRgShaazDiLmbTxyupLDqIUAACAASURBVDvhxetY8dQ9qhfC9M7lkcXMF1YmW8sWT7ohW7rLvXPnDpydnXHp0iXs2bMHs2fPRuvWrZMQWLFihQyNb7/9FufPn7cMJRNqx8XFgZy8nJxSX1KQYn6zZrU+QcW+TUDPP87iWvDrJGTm9yiPBn45sO3SU4zddE2C2NAGPhhQ18dqTm/GpsMWz2ysT/48cyFA362UtoSEBMTExGDkplsIuPVS0v2GT6qhVF53nLwbin4rzyfd5/pkd8VffSpbReI0MjISrq6uZpO1JXjFxsaKfsn3I7XM0t+VdEO2ugCPHj0adKy8ZMmSpI+WL18um4epU6fi3DnpHaItJ4sWBVlqky0RPn05LF0gSlgtCLiH3w7elXxEIudHR9fBibuh6L/yguSzmR1LoGnJnCn2RXF3d7flFHPbmRwB+m6lFtlGR0djxr4H+Od8cNIsuDrZY+vg6sjr4Yy280/h3stEMQuNfVLXB8MbF7V41uiZ3dzcUoVs6SXDzs4uxX5DlMCy9Hcl3ZIt3d2eOXMGf//9t8FFxMfI1j9GnrHzOhYcvC3D/c70Nuj352nZnS0lDjgyup54K2ZjBBgB8xAweIzc1A8jm5dAkXHbZY1/UMNHHB9banyMbBmCaYZs6W2RjmB37twpnKD27t0r3mQ08bb0t44dO6Jw4cK4fv06PvroIwwcOBCfffYZk60CAoQnfTly57Y+2c7ZG4hZe25KeiW94mPjm6LZzwdx61ny8TIVIpemq5OaMNla9l3l2pkcASLbJ89fov6v8oxYQ5v64YvmJdDut8O49DBMgtSwJn4Y1cKyjD/UoClku/tKMHZcegIS2GhZNg/eq2CZLnNERATs7e3Fzjq9Wpoh28DAQLRp00aCY4cOHZK8jzt37izuajVG/z9lyhRQ+I8h452tdcg2LCoOgU9fI2c2J7T6XwCi4+IlsHetWhAzOpdH94XHcUYnDy0dIf/WowKTbXr9leBxpwkENKE/rRecx7OIaMmYfupWEd2qFhROhQsPBUk++6NPdTTWErLYd/2Z+I6SjGOnygUQGhmLfJ6uII9/Q6aWbHdeeoJP/zoraern9yuic5WCZuPIZGs2dOZVJMBfvXoldmtqjySZbE0n26O3X4ov7dXH4WhbIS/yerhgUYA0ZEdpBisV8pIp29Dffu1SCrk93VTPmXmrg2sxAhkbAQ3Z3onIgs/+OpdEuN2rF8IPXSqIh/ebuAOkwKZt/eoWwTftyoo/rT71AOM2XFQEqmnp3EJC9X/+gSBdZapHIjIaU0u2Hy89iYM3pXHAPtndcGhMY7MniMnWbOhSriKTrTqy/fdKsNBSpTjWxYeDZMmnzZ2xvV80RC7nBOHYoPYFydy+uB4jkBEQWH7sLm4/fwPK5kMnRsVyJTr86eazjYx9C2cHe0migaLj5Ik7etcujG87lBNtlPxqpyBStTa0SXKCA7Vk223BMZy6+0rShXdWJ5z7urnabmXlmGzNhi7lKjLZGifbbzZfAX3BLTEnBztQSJCurexfExXyOCWR7drTD7D94pOkIyxLc2xaMmauywikNQTGrL8I+o5ozMXRDvu+aCQSCqhJHj963QWsP/NQ8lh0RExhQR0rF5Spuxl7fiL8q9+2EsXUku2Sw3cwddtVSdOWiGlQQ0y2xmYqDXzOZGuYbL/fcR0LD8k9i41NXSFvNzwIiRTOTx0rF8Cwpn6gpNXaRndC9EWNiXwtyPafi88xUUfzePYHldHewqTWxsbKnzMC6QGBhHfv4Dterms8/D9PYzVkS9rIEzddxtpTD0Dt6ZqDfRZZjmhD2Hi5OeH8N4k7UrVkS2X/539TZO2i1+++dYtgfOvSFk0Bk61F8KVMZSZbZbK99iQcu688xdz9txAXb/hYydHeTlJmYH1fTGgr//KQ48WQVedAx1vebk74rWdlkUJPk2Kv0S9H8TRc6thBab+W96uRMouBe2EE0jAC9D30m7hTNkJyLCIHIzVkq12ZMmdpEsireWzfXFkR9Fwq1jGpXRn0rZsYo2sK2arpz5QyTLamoJVKZZls5WRLzgvkxGDIKhbygpO9HSr7eGFgA19Bolcfh2HBR9VQp1gOg3XpjVpbw1hDtnV+OoyQyETRD43VKZYTqz6pmUqrg7tlBNIWAu1/O4yLOqE7NMJGJXNh8UdVEBYWhhw5DH//NE9Ua/peIaeqxqoV8cb6wXWw63KwkGGlK6E25fOBnK80xmSrBkn9ZdJM6I9lj6G/NpOtnGzpuPeOTqo7yRux1m7zwoNQEc6jCfXJkdUJ6z+tg6I51ctAasj2jxOP8eOu65LJmtapHD6sWdhW08/tMgLpCgE6+SFP4zP3pA5G9BB7R9aDl8Nb1WS7KCAI07ZLpVP1gTG7RyW0r1TAIFZMtpYtJUWyXbdunQixIdEIjWg1JQFYu3Ytnj17hvbt26N///4iyDitG5OtnGyVPBa153FEMz+M+C+DSM9FJ3D0tjSDSM+aPvheTwIBpfWgIVvyRv5t3y3QjwDd51Je2n7/HVGl9XXE42MEUgqBeftv4cfdN2TdLf24KirmdjRItm9i3sLNyUEk+iCbf+A2ftB5waW/Vy3sDboeon8oPrd9JeOiE0y2lq0AGdnSD2PVqlXRs2dPIRpBRrlmKctO9uzZkStXLty4cQPDhg3D0KFDLes9BWoz2crJtsTEnYg1cE9LJNinThH0/eMULj2SqtHQlFUu5IWNn9dVPXvaZKu6EhdkBDIpAksP38G3Ot68BMXagTVQzNNOkWwP3XyOQSvPICo2XmyQfuleER0rFRBJUYoqOF31qlUY33VMDAdSa0y2apFSLicj2+PHjwspRJJNLF68uKhFmXMoo86hQ4dEsnZKgbd06VJcvnxZZOFJy8Zkm0i2lHZrHYUUZAFm+wdC7qeYPIvkWXwjOAIkuaZk5DBBjhNqjclWLVJcjhEAZu8NxM86cqiEy6oB1VHS215GtnS/WurrXTLvY4pxpxhd3wk7kEC6iVr2eePi+LJlsmCFGtxTi2wP3HiGE7efCz+Q/g2KWyWDkZrntXYZGdlSKjvKqHP16tWkDAvvvfeeyCGrSWFHCQB69OiB3bt3w9fX19pjsmp7mZ1s11wOw+KAOwiPfivectVYNhcHkbhdqXipfB74+5OawttY1ygH7fSd13Hs9ks0KZ0bE1qXBnk4MtmqQZ3LMALApnOPMGKNPCUoJfM4NrYRXkeEC7Ilgp205Qo2nHkIr6xOeKbj5U9YjmpeQoTkKe2U6RqHYncntCmN1uXyqoI+Nch25Yn7+EorXJDEMXYPr4/cHoalJVU9UAoXkpHtpk2b8OWXX+LKlSsiTRylNipXrpy4v6W/kz148ABNmjQB3e1WqlQphYdsWneZmWx/3HYR849IA9y10aMvHMXlqbWC3q4IGNMk6T5Iu15UXDyqf+cvSFpjlJzgyLgmeB0RwQpSakHmcpkWAXoZLj5xp+w7WS6/B37sWhElcrsleSP3+/MU9l17ZhCrknmzCW/iMvk80WvxcbzV811f2qc6mmhpJ+tr1BZke/5BKNaefiikJ6v4eOPThr6SFH7FJuyQ4aGtapWeFouMbM+ePYvu3btj2bJlqFu3rjhOpvvZBQsWoGnTpuLZDh48iAEDBmD//v0oWNB8cemUACozk23FKf+KHa0+s8sC2NtJY2iNzUmHSgXwaw/5C9YfR+5iytYrsurrB9dGiewOTLbGgOXPMz0C5EdB/hS6RrtT2qVq4mzJd0bpHlYfgMZeqj9p4IuJbRLj5qPjEjDz3xs4deeVOJXqU7cIKhb0Ep9Zm2xvP3+NZrMOSq60tH9f9N03D25YDONal0p360VGtgkJCcLbmJygWrduLe5pySmKvJE13sd0zEzHzZrdb1p+6sxEtseCXuJE0CvQMfCHNX3EPY4tbMuQuqjw3xdQ0/7K4/fw1abLsu42D6mLoh6JSZ9ZG9kWs8FtZiQEqk/zx/OIGMkj/dilAt6vXkgiaqGUt9ZcHCiWfkr7cqhQ0BNdFxzDaS1dY1KcOjK2CfJ4uFidbOlemu6ndY3yYmuiYN6bHYDLj8MlRWZ2qyg0o9ObKYb+PHr0COPGjQM5SzVv3hyDBw9GhQqJWSWIYCmvbNeuXTF9+vQ0/7yZhWwXBwThO62YOmNvs4Ymjr50SoH1mjq00GnBaxvdIdX/cb9EIcovtzv2jGrId7Zp/lvCA0wrCBwPeon+f54GhfCQtSqXF+NalQLplx8KfI5iOd3wXecK+Ov4PWy7+MSqwyZSH6OQEYji4Cke3to7W9pBUyignGzbJl1VBb14g8ErzuDm0whRjKIkJrdPzGCU3sxkUYvY2FhERkaKPLLGcsmmBTAyA9nq01Q1F/8b37XGe3MOI/C/Ba7bDsXobfi0jqz5B68i8fuhIJGajwibQohyujsz2Zo7EVwvUyJAfhS3nr1GrmzOwvO24U/7ce9lZBIWFEJLzk2PQqOsio+zg53ejEC3vm+DkJcvhHOWnZ2dVfqdsy8Qs/69KWmLNgm3v5fmNacCL0PD4OzoAPes6sV0rDJIKzZikGyjoqJEjO39+/fh6emJ8uXLw83NTdL9okWLRDhQu3btrDgs6zWVGciWYutKf2OdI2OSYlz1SS3hUdxz0XHFECGSbyQvRrXG3shqkeJyjIAUgVv/3WtaGxeKJtCVTqU+yhfwVIytvzCpBWJfh1qVbGfuvoHf9st3tkHT20jkXmlcGVYbmS7iV69ejZkzZ+LNG6kwdZUqVfDFF1+gRo1E8fgxY8YgJCQERLpp0TIK2f5z9hEuPQoV+SspLV1eD2f8ffI+HOztkMvdGV+su2AR/PRWS4LnFD/r4pioDParfyB+8Ze+eVKs27WprUDl1RqTrVqkuBwjkIiA/7WnoCPlR6HR2HlJ3XExeRTT8TPlpTZkpHlcJEdWzDsgJToKq5nSviyG/X1OUl2z27T2MbK+3xciW13LsGQ7b948/PLLL6hVq5ZQksqfPz/i4+Nx584dLF68GE+ePBFhP0RkFINbtmxZ/PDDD2nye5IRyHbOvluY9W+yfBsdI9EXQJ8rvzkTsXJATdQrnlNSNTI2Hu/NCZBkAvmxawW8Xy1ZnFxNX0y2alDiMoxAIgLbLj4WiT9MMVdHe5z7pjnO3Q/FB4uOy6qS/Gq/ekXFSzKRce8lJxSb/6JFCdnRLhWkq6XwkJdW3dma8vuSIcn26dOnqFevHvr27YsJEybIJoR2vRT2c+3aNXF8TOIXRMANGzY0ZW3oLUvu3kTsDg4OimXo7crd3V21Z2tGIFvKcamUm1It4HTvQ//QPZCSkafh0XFNBIHrGoUjLDtyF/TFqO+XU2iqmmpMtqYixuUzMwL1f9gvckWbatuG1sP6sw/F91Xb6Ft9ZFxT5PdKFIIYtfY86KRMyTpXKaD42aXJLREdEWJVsqX+1f6+ZEiypdhZErA4d+6cIDUlu3jxIrp06YKSJUti0KBBIkRIHzmaumAopIiOrwMCAiRV6e6YSP7u3cSF1K1bN6HdTCElhiwjkK013PxJJWbnZan8IrnXNy6ZS9y/Fs+tPNemzp9SeSZba6DIbWQWBEp/vQskEqNLmOrlZ6RI6To0knfvLj1SrEoY05HzgS8bWd0b2ZT5zJBk+/fff4sj4fPn5ZJhGnBod1mnTh2sWrUK1atXNwUzvWWJTGk3TepUtGPWJdt+/foJ8qex0TF2586dBdl26NAhw5Ntv2WnQInZLbVpncqDPABfvY4VyjLkQq+0m7W0H936TLbWRpTby8gITN5yBcuOSnenljxvq7J5seCjqklNrDh2D19vlsfEK/VBDlO/dK8kXsatfWdryjNlSLI9duwYevfujcOHDyNPnjyKeBw5cgR9+vQB/Tt3bnlWGVNA1JSl4+kXL17A398fv//+u4RsKWFytWrVsGbNGpCDFhkRLZEuKVtl9J1tRPRbjFxzXjhNWGLkZWws8bsl7eury2RrC1S5zYyKAKkqfrn+gtA9piNgumeNfptg9uP+2a8GGpbIJalPvycbzykfJWsKUnif9rWRLcn2zL0QBAS+QAFvV5HyT9cyJNkSsdH9K+1YZ8+eLbsbpTy3JOdIx8Yk5Wht2759u8gqpL2zvXXrljiq1iZ3kpPcuHGjULLSmOaIWXtMJMpB98spZRQuRffOuiFSlvZP963D114U2XjMtfWDaqFSIU9zq5tdjzzaab2kVIYoa11pmP3AXDHDI0Cbg5Swb7ddw/Lj903qqlbR7ChXwEOEzzTwy4lavtkl9Q/efIHBf51D3H9pNkvkyZYkGqFdkE6/yufPhh7VEx0iKerEy8tLol1s0sD0FF4YcAc/7k6OeqhcyBNrB9aSaLDTbwgpGKamtoOlvyuKcbZbt27FqFGjRP7a999/Hz4+PoiLixPeyERyZJSwgLyQrW1KZKvRaz59+rSI9yWj0KS5c+dKSJnudHWNdJxJCSuljOQuycwN/H4TE49rT18jn4cLSCrtavBr3HoeiUXHHpmUNEDpeQfWKYBBdeWexDFvE0QeTC83w/ff5mJIDm90P2wuJqb2S+tWI/dmal0uzwgYQ4BepmnTYWvbd/MVvtwsDb0z1meebM5Y8VFZ5Mgqz8p14FaI+C35/ehDWco9Q+22Lp0T371XXMhFEuFZ87tFhF/r55Oy7ie0KIouFZNPVi39XTWGm5rPSdDDEtMrakHE9tNPP4GITtso2w/F1hYrVsySfvXWNbSzPXr0qNBpJlPa2So1mpYcpOhLqrtQrweH40lYNAp6u4n4tmtPpDqg1gT5s0bFMKaVVMB77IaLWHPqgeiGPJYXflQN1YqY7nFsaJx8jGzNWeS2MgsCv+y5iV8VtIN1n58cmDpWLiCOm/vXKwonrRh4yqrzOvqtaOeUluaxqRjenNYaYa+sG/pDY3j1JhZVpu6RDYdClUY080v6e4Y8RtZ9apJnpLtR2kKT45ImGYEScZg6gUrllchW6c528uTJCA4OThd3tnTXOnz1eRFwTncSv7xfSRDa+78fl4h+WwM/Q21817EcetUqnFREKXdmXk8XHB+fmN3JWsZkay0kuZ3MhMCiQ0GYtsP4FdjC3tXQoozUv4ZSXb6/4BiuWunl/eLkFoiJsK6CFM0l5cwu+dVOEQKkbYs/roZmpZOfKVOQre7iDgoKAhHi2rVrsW3btqRjXUu/BETedFRN98AU+rN3715x7Kg5JyeHLA8Pj3TnjXz/VSQa/LhfAk9WZ3sMaeyHH3ZdtxQ21fXJ0eLSlJZwd06OX9aXdYMC2E1RiDI2CCZbYwjx54yAHAESrenw22Fc0cl6o11yYtvS+KS+r6zyjJ3XseDgbavASnmsD49tYjNv5DHrL2Lt6cTTNTL6jSJypztnjWUasqX7CSLBDRs24NKlS+L5Kdft/PnzVYtLGJv1wMBAtGkjlemisB4iXjIiebqTpdAgMgr9mTp1qkhwb8hS+xhZSZKMxmtJVh6l561WJDteR8fhenCE3rbpWIaOZzQ2d/8t/LQ7WZmK/k7LO2h6ctYNY/Om5nMmWzUocRlGQI7A7weDMH2n/t1tsVzuaFE2D07dDUE+Txf0rOEjvv90PXTnhVRq11x8J7crK/La2sIbOS7+Hfwm7pAN7dsOZdG7dpHMQbbR0dEiSTx5/NIuU2MkYkGhQdYK+TF1AdDRMcXb6hPc0G0vtcl21Yn7mLAx8QXFlvb3wFqo7ZtDeELT0YzvBPkC/rxxcXzZsmTSMMgxSje7z3cdy6NXLR+rDpXJ1qpwcmOZCAG6ghrw5+lUe2LyVP6gho9wnqxTwBG5cua0qqNjpr6zpVhXCvnZsmWLSEJQqFAhdOrUSexkKeSHNJErVaqUapNvasepTbYks9jyf4cQ+FRZKtHU51EqX7NodqwZVFvyER1d0xG2tinpGpM34J9H7+J1TLyIwa1RVBomYI3xMdlaA0VuI7Mi0P63wwbzS1uKCx0TU8J6evnWWPMyeeDmZI/dV4IRHZf49yLZXbHhs7rI4e5saZdJ9WljUHbSbkTGSkOpdGODM+Qx8pkzZ9CjRw8UL14c06ZNQ+XKlYUHrcZJicnW8DqjFxTaXWp23sFh0ag9Y6/YbVrLfu1RSRAphQnlcHfCgHq+kpg06uejJScREPhc0qVm92utcahth8lWLVJcjhGQIhAeFYeKU/5VTHVpKVZ01+vu4oBBDXxBwjnLj90VyU1oN9upcgG0nR0guy+mOnRPbE1r9WsArus4cpE8JHlZayxDki3djX788cfC05e8j0kDuW3btuLYmFScmGyNk21YVCzuhSWgdD4PrDh+VzGLhiWL9cqUlsiq5eik2xaRfdHx8mPkIY2LY7TWMbIlYzClLpOtKWhxWUYgGYFFAXcwbftViyBpUCIXDt2UvniT85FSKru7L97gn3OPROKT3/bJc83SjndR72oGx0MbixXH7+HF6xjkyuaMj7QiIHQrhkfHocLkf2XtZZrQHwogpkQEdJRMCk20WytSpIhIArBkyRI0aNDAoslPycopfYy85OBNTN0ZmPSIfrndEagn2445OFAM3Y2prYwGlislLxjaxA+UQiuljck2pRHn/tIyAvEJ73DqXghcHOxQqZCXwaFuufBYll/W1GejrF5Pw6Nl1Wa9XxEty+ZFVicHcTJ27UmESKlJ49NnAxv4isQlZHQF9d22q4Kci+Z0B+XTJTt86zlO3w1JaqKWbw6sHlhLsUkKh6RjZF0b1bwEhjXNZHG2MTExwlGKFKP27EkMPq5Zs6ZIAEB3uZZKWJm6cEwtb2uyDXr+BpsvPBLHxOXye2DgijOmDtGk8kv7VE9a1IYqjlh9HpvOJ2uf0pdp5/D6KJXXw6T+rFGYydYaKHIbGQEBEq3ptfgEXr6JFY9TMm82rB1UG56uyuptMXEJKPm19WVxtbEkpTo6Hj57PxQngl7qhdkvlxvWf1YXnq6JESADlp+G/1V1eu27RzQQz6pkPRYex3Gtfik375FxTYTIjsYy5DGyoQVNIUC7du3C+vXrRQiQtnxiWv0iWJts6cuy+tQDPAuPFpkwftt/y6r3sUo40hsevQGT85J2nKwhzOl04sftF3H9RRxyZ3NC9+o+ZuWitca8MtlaA0VuIyMgQIndj92WEpqhe1BSmGv1P2m6USUcKGSPfifCo9/ijyN3JEUK53DDvZem58fVNLKyf01kdXFAQZe4pHy2+q6q9M0RHT3TEbSSxb5NwC/+N3H5UThorL1rFxb3xtqW6chW++HpSLlgwYKZamf7KDQKjX46kCTgnRJf/kYlc2NZX9PTGNKXgeLiUitESxsbJtuUWCncR3pAQOl6p55fThChKRnJLXace0TVox0b3wS5srmgx+/HcPpe4jEu7Zj/170S+i47paoN3UJ0t3t8QlOsPH4Py4/ehYerI+iIt0Ol/Ip+Ifo6uawjqGPqYDI12ZoKVmqVt+bOVq1WqbWelVzyD41pLFFSUds2k61apLgcI5ByCJT6eheidRLDd6pSQEi4Ktm5+yHoNO+oqgHSb4W3m5O4fz155xUWBwSBRC9ol0h5rJ9FxKhqR7eQk72dTE5x3odVRArAvSrybNNx8KmJzSzKnc1ka9bUpWyl9Ea2JEwRGhUnjo1JhIII1xxjsjUHNa7DCNgWgaLjt8uuner75cQKPTtb8gomb13SOjZkeT1ckDObMy4/ChPFiHCtGW6o2zclPqDww7P/7aCNoUY7d9rBm2tMtuYil4L1rEm2tLA6z1f3lmnuI24dUg/lC1qec5bJ1twZ4HqMgOUInLjzStzNujvb4+M6ReBobycapePc/Tq7wUENfTG+tXLsKhFmryUncOTWC8sHZWYLzg72iHkbL6lNu/EnodESxyYqQD4lSi8GJLpD4jvmGpOtucilYD1rki0Ne+LGS/jrhGnJnNU+roujPa5PbaW2uMFyTLZWgZEbYQRMRmD5sXv4ZvPlpHp+edyxbUg9ODva48GrSHz8x0lQFANZ5UJeILEZ+u4r2aQtV4TCW2oZvSh4uDiKY2hto1ScFx+GCgdRbVPSfHewy4LAaW1kwjumPBOTrSlopVJZa5Ltufuh6DRPnbOCuY9LLu8FvMw7Otbuk8nW3BngeoyA+Qgk6pLLj4opvp3i3DVG3sFODlmQz9Pwd734hB1C1Sk1bWqHspi05aoQuiCjNJzbh9bDoJVnVacI3fdFQ/jmcjf7MZhszYYu5Spai2yVcr/a4ilal88HEsIYUK+o8Pwz15hszUWO6zEC5iNAsoflJ8tFGoY2KY4vWiQnAVHbQ+lvdiEqVnqEq1SXxCn+vRJslqxj2fweBtP4KfVH4ha0+VCbkF4p566mXWrn4M3n4gj64zqFk47ctfu1NtmSuhWdGNCLjF/ubOhcpYDaKTG7XJZ39Kucgc0aZEuxaxUUvkC2hM0nuxv+HdlA7/GSsb6ZbI0hxJ8zAtZHQOxsyQlKoekcWZ0wp2dl1Cmm3lFIyXtZ0zQd71Lqu4oFPdG0dB48DInC+jMPhLrc07BorDqp7rrLf1RDkft228UnMk9pfQg1LZ0bLcrkFan81NjUDuXwUe3CsqLrzjzEl+suJP2dNhpbh9aHi2PiHbfGrEm2IZGxaDrrICjjkMb61i2KSe3KqHkUs8sw2aqA7sCNZ+jzh3lxaiqa11tkbKtS+LRRMbOaYLI1CzauxAhYjMDqk/cx7h/ltJrkKEXa5iS7qsZKfLUTJPqgbW0r5MdvH1QyKNlKIhGUS1uN3fq+DSJj3gpynrPvFkhC0ZgNalgM41uXwppTD0Ti9zM6XslE+Lr7OPJgpphfbfMdvyPpeFrzd90jd/q7Ncn2f/6B+J//Tdkjkla0dsJ6YxiY+jmTrQrEHodGoc6MfSpKWreIrhi3Ka0z2ZqCFpdlBKyLAIlRzNh5DceDXskaNiX71vc7rmHhoSBJG7/2qCxEJQzZz3tuYvZe42Q7rVN52Z8zzQAAIABJREFUlMnvIYQwtFPsGUMjYEyT/7d3HdBRVF34QkIChEAChN57L6H3FjpIE5CmVEGKgCIKSBNBEERAOiIgTX66SO+99w6hhBZaCCUEQv3P98JsZmdnd2d3ZzebcO85HjX75s2bb968771bKXPKGHvzjksP6N8Tt0U5vmr50gjyhnOXUo4Orkk44UOQWzn3INNUlGoqdz3J9vctl2miCtleGlmPvDyQi8s5wmSrEVe1clMaLzU0Q+xsJv+k9N+pO0aXwoMvjW9iCn3ywujvK7tXoOJZLCcqNzcGJltb3w63ZwT0RcBcEQFl+Thrdx278aKwL6LSV9fyGahjVesl7syd3qR74eS5+ZvK9O+JOzRtxxWbs+LJbbCItw2+HyHSwUo5ns3dXxlvW370Vrrz2LhIwtjmRal5iUxGsOhJtgi9UmbUyp3Wlzb3dW6BHSZbazOdiNacvEO9Fh/X0NJ8k2ypfWj2FyXpyYs31GzqXiObzs+NC1HRzH6E4gFXHkQQMrZgwlnbvVoaEJOtQ6+LL2YEdEFAWfgdSWtwsrVH3rx5I+qKp0qVyuLlsEk+jnxN9SftMSnKLr9wcP38NGLteXuGIjLbwa+kx8JjtPZ0qKEP2KQbFslAK47dpm/+d8Kk71PDaolQIkmgfu7y9xGD/bRxsYw04TPTbFp6ki3ujdq9wz54WBdIn5wmtSouct07U+IM2Y4aNYrmzJljhEVgYCAtWbLEIj56OEj9uOqMyA3qiMCh4I9WgZTUy0OUslp/JlTYNIpk8jNK0I2/YdfpqDDZOoogX88IOI4AvF1n7rpCz6PeUupkXtS+fHa7402tkS3MXYjhvXwvQtPA4Vh18lZ0xilb5JOiGQQ5bTxzl7ouMK5yhqULMbWIrW05Yz8huYckfYNyU+8g4xKfGHOfJSdEekkcMoY3KkitSmcxGY7eZCvdQK/1Vgt+cYZsR44cSTdu3KABAwYYnitx4sSiwL0l0YNsB608QwsPOka2GCPCeqa1CVQdblhEFP303znhEYid1oB6+al8Tss7WEvPzWSrZfpzG0Yg7iBgjWxxQtysseRdw6IZRLrFkzcfawKgZLaUVDx9EiqTOx0FFYhec82pig8OrEGooQtZf+YuXbz7jKrkDRAJPJTS8I89dPpDiknptzkdSlG1vNG1cSXRm2wRajRy7Xm6+jCCmhTPRMMaFhBqemdKnCLb8PBwGjdunE142Eu2Z+88pYErT4vJiHOmpfgoJKFADN3SozfpZlgkeXsmoEeRbwjqHKVcH11fdfwNJu2hM3didpnYIe7sV42ypEpq0/NKjZls7YKNL2IE3AYBFHFHaM3yY7fIM2FC6lE1B7ULTG1WjayWd1n5MDBn1SmYjvrXyUuzd1+jkeusq5FR/H1ex9L0NDzMUGIP/ZqzSV8eWVc1VlY5Fpz6kbRDKSgViMpCziJbkDtIXi6WCtzrNSHiFNmilm65cuXI39+fgoKCqFQp66Xn7CFbZEopO2qr5ioZF3+uS94fXPmfP38u1MOTdt008SI0l47x2cvXVHjYJpN3yt7Iek1z7ocRiHsIIHwIYURyGVgzO31ZQz0eNP/gDfRCUVFIfi0yOCGTk1zGbLgg1ql3795Ti1KZRSiPUvoG5aHeQblFyU7YixMmjA5bQgIP5B+QH0TypUtOG/pU0gQ2YpKxQVBK7xq5qa+CbFccvkan7zyjpIm9CafyfGYK0Wu5sbnqbVo3CVruodYmzpDt6tWr6dq1a+Tt7S0K12/evJkmTZpEdevWNTxXx44dTZ5x9+7dtH//fpvwuXg/ktr8rR4np+yoQLpk9HfbgoY/o2g75Ny9SGq/0Nj1/fugbNS8mGkB5bDnr6j2NFMHrC/LZ6Ivy9uf2QRqJ09P56pGtAArYSJ9pFqucaQNFgQ97N6OjIGvjb8IYDMdFmZcAN4ZT1v6t0MmMajVcvvT2EbGpz7p3iXHHTQ7jBypk9KoBjkpV2rLmrIf1wbThvMxz+aXJBGt6FSEkif2pLdv35KHR0wO578O3qGpu03JeXuvEuSrUSX769br9L/j9wzjTuLlQcs6FKG0vtHhQRD8jnaSQNO44PPClDeNfVq/Gftu06x9t0yw2tu7pMhfbU5Sp9aejCROk61y8P369SOolWfPnm34CTZdpdSoUYMuXLhg07eAvKXVx+/SdE378lkJXn0Q2FuH/3eOwp+/Fp7En5XKTDsvPaQ3796JLC91C6nbl59FvaFiP20xud/X1XNR7xq5NI1D2QgLAvBJmdL+Sht23VjlooiICEqUKJHYKLlC5AuCK+7H9/j4EADxOFuKj9hKT1++NrpNw0IBNKFVCdVbt5x1yCRXMTyGRzUpSPCCtiQ/r71A8w+EUCLPhCIMsUa+AErq5UmtSmcilO+DPHr0iPz8/Awn24lbg2nSNuNCBGi3+7sqlMGG/O7/O3KLgh88p8SeCenTEhmFl7NcCgzdZBID3LVyDupfW33TYe29TNwWTJO2mo77wk+1LKq/HV1X4szJVgkgbLdHjx6lxYsXW8TWmhoZ2aFm7LpK956+pKp509DAevmFJ13TqXvp2A3rzgM9q+emfrXy0PaL96mDIstU9Xxp6K/21lXdeIA6E3bRhbvPjJ5l27dVKUeAj7W5o/o722ztgo0vYgTcBgE4ZcI5Uy7fB2Wn4PDXglSR0/jLyjlF7WvIqVtPqPWsA6ol7poFZqLfWhRVfbZf1l+gGTuvGP02onEhalfWOL2iUo1szkEKheIDfPXbWGf7wVTVjDSVwxrGaBRteWnHboRT06nGpVIRI7z8q/K2dGNz2zhDtiDXxo0bU9asWcVJtV27dvTll19S9+7d7SbbfVceUutZxqqXynkC6O+OpWnNqVDqteiYVUCl4O4x6y/QNMWExcXmHKKUHd998pIGrz5DW87fo+ypfIQLfKXcAVbvb64Bk63d0PGFjIBbIHDt4XP6dNo+gpkJUihDcrr/7CXdfxbjeAlfkcM/1hRqXggyOCHUCBmklAIyAakoRc3Wq1bQXkm250KfUr2Ju426A8mCbPWUzvOOiHVRLmqJL2y557YL92nI6rN0OzyS6hdJT8ikJSXksKUfW9rGGbJt2rSpsNVKgv8fPnw4IfzHklg62Y7ZcJGm7TBVJ5z7qQ4VGLLBKo5Nimek3z/k+hy78QJN2W68O7SFbK3ezMYGTLY2AsbNGQE3Q6Dd7IO0+7L1ovHQrEHDJgnCWr7465DJ0yBiAqkQlaJW7KBKngDhgSwXJdnit3WnQ+mb/50UBQyypfIRCSmkk7ZecEKV3n3+Edpz5ZGIDOlpZwUlvcZjbz9xhmzxgIi1gt0gTZo0lCSJtpqvlsh29PoLotqFUrADbDbNWM2gBvCMtiWo9gc7rJoqhsk2GrWnT58Km63Wd2bvZObrGIH4hICa+lTt+ZQkGv78FRUfsdmk6ZpeFalwxhQmf1cLGSqZzZ+WdTNWq6qRrdSZs5ND6B1nGxvzJE6RrT0AWSJbtR1guZypaGqbQCr+k+lkld+/fuH0NEWWoELNnRxB0qjwERvCJ9vYQJ3vyQjoh0DN33dazQaFKjWHfwwyJPeX7v7X3mv005pzhsGgPvaPDdRDhmC/hB1TLq3LZKVRTQoZ/c0S2er31Oo9Mdk6G2Ed+rfmILX+dCgN+fcsPYx4RUhDNrpZYUqSyENkc/przzXDCFCDclrbQFFKCjk0lR5zKEvVeMo+unw/xslpZrsSVKug5QxXOjyiahdMts5ClvtlBFyDAHxK2sw6aIhjRbWcH4Ky0YozYXTgahgVypCChjQsSKWymdphMULUaz1+I5wKZUxhyOikNvIjIeEitSKSaECQu3hF9/ImuYKZbB177x/1ydYadPuCH9Kh69Hk2qBIemvNCRlR5uy6LDJHNSuVjXIGODextaUBMdlafV3cgBFwewQQJYFEE3CEalUqI71+8dxqIQJ7HgqHjcUHQ8jTI6Eo8p5MJU6WydYeZGOuYbLViB8ys/RadFx4xcFIj6Lu/evkM7layiCVLFnsES0GxWSr8cVyM0YgjiBgLTeysx8jtsg2IuoNdZ9/mHYFPxJFHHrXyEN9gmIcwpz93Hr1z2SrEckei47R2lMxpaRw2S9NC5tUqGCyNQWUHaQ0TjJuxghYQOBjJVu1AgvjmhelTxU1b9198jDZanxDap6B8tAfqRsmWyZbjVOKmzECNiHwsZKtalKL8tlo2Cf2JbWwCXQdGzPZagQTcbeRr4xTtH1eLhv91Mj4hTPZMtlqnFLcjBGwCYGPlWzz/riBot4Yr71dq+SgAXWj0+TGFWGy1fimFh28IUruyWVl9/JUPIuxJyCTLZOtxinFzRgBmxD4WMl2zt5rNFwWxgSfGcQMw8s6LgmTrQ1va8OZu3T0RjglSpiQ6hZOpxogzmTLZGvDlOKmjIBmBD5WsgVAyw5dpbOhEZTE20ukVyyYIW4RLZ6ByVbzVNfWkMmWyVbbTOFWjIBtCHzMZMtJLWybK7HS2lpSC70HxWTLZKv3nOL+GAEgwGTrQUmT2lfD1h1mEJ9sdX4LTLZMtjpPKe6OERAIMNky2br1p8An2zSx/n44zjbWXwEPIB4gwGTLZOvW03jgwIE0atQol40xKipK3MvbW7/iyfYOHnYOX19fey/X7boXL16Qp6enqPzDwggwAvYh8O7dO8K35OPjY18HDl6F9QSZ8RIgjZOL5eXLl5QwYULy8vJy8Z31u128VyPrBxX3xAgwAowAI8AI2IcAk619uPFVjAAjwAgwAoyAZgSYbDVDxQ0ZAUaAEWAEGAH7EGCytQ83vooRYAQYAUaAEdCMAJOtZqi4ISPACDACjAAjYB8CTLb24cZXMQKMACPACDACmhFwO7JFUojXr1+Tn5+f6kOggDHcz5MkSaL5IbkhI8AIMAKMACMQmwi4DdnevXuXhg0bRgcOHBB45M+fnwYPHkwFChQQ/x8SEkKdO3em69evi/9v3rw5DR8+nGM3Y3P28L0ZAUaAEWAENCHgNmT7zTff0OPHj2n69OkieHnIkCF07949mj17tniQjh07ihPtmDFjKDQ0lJo2bSrItlGjRpoelBsxAowAI8AIMAKxhYDbkG3Lli0pW7Zsgkwhy5cvpwkTJtDu3bvpyZMnVLJkSVqyZAkFBgaK30G0IF2QMwsjwAgwAowAI+DOCLgN2W7ZsoW++uorqlmzJjVr1oxGjx5NXbp0oRYtWlBwcDDVrVuX9u7dS2nSROf6nTt3Lq1cuZJWr15twPfmzZsmWIOQS5cu7bJ3gJRq79+/Jw8PD5fd09yNYPt2hxSJb9++FSneoLH4WMVd3gXwd6f3gW8F40E6TxZGID4j4DZke+vWLerQoQPlzZuX9uzZI3ILL1iwgFBI4NixY4ST75EjRyhFiuiiwf/88w9NmTJFnHwlwfVKQV+XL1922Tvkqj+mUHMhAqKHDx+Sv7+/W2zC3Kk2aGwn13fZwsA3+ugRcBuyhQ22WrVq1KtXL8JiMGjQINq1a5cgWDhF4WS7b98+CggIMHuyVXubXPWHq/64w1fOZKv+Fphs3WF28hhcgYBbkG1ERAQVL16cpk2bRkFBQeK5z5w5Q02aNKG1a9dS2rRpTWy28FyGB7M1my2TLZOtKz4ka/dgsmWytTZH+Pf4jYBbkC0grl69OmXPnp3Gjx8vYmh/++032rZtG61fv17Yc9q3b0/Jkye32RuZyZbJ1h0+YSZbJlt3mIc8hthDwG3I9ty5czR58mTavHmzqNdYqlQp6tmzJxUtWlSgc/XqVRFnKzlBQe08YsQIq/UNmWyZbGPv84q5M5Mtk607zEMeQ+wh4DZkK0EAlTLsOOYySEF1jHhb/KNF4grZvnv3niZuvUw3HkVSmuSJqXGxDJQ/fXItj6jaBl6eyLYleW/b3ZEOF37MDlJn7zyltafu0JNnz8k7cWJKljgRda2cg3y8jb1vd11+SHuDHxLKclfJE0DlcqbSAXn1LthBymnQcseMgFkE3I5s9X5XcYVsW844QAevhRke3zNhAtrVvxpl8LMvLSWTrd4zyfb+Tt9+Qp/8sYfeKy7Nk9aXNvSpRAkTgFqJNp+7R13+PmLUam6H0lQ1b7QzoN7CZKs3otwfI2AdASZb6xjZ1MKe0J+wiCgq8fMWk/v0CcpDfYJy23R/qTGTrV2w6XrRL+sv0IydV1T7HNOsCLUslVn8Vuv3XXTp3jOjdkH509KfX5TUdTxSZ0y2ToGVO2UELCLAZKvzBLGHbK89fE7Vxu1gstX5XcR2d0P/PUvz9kXn8lZKv9p5qWe1XOLPhYdtpGcv3xg1KZ7Fj1Z2r+CUR2CydQqs3CkjwGQbF5Ja5B+8gV68fmv0suZ1LC3sd/YIn2ztQU3fa5YeuUXfLTup2umhgUGUJrm3+G3Ef+do9p5rRu1618hNfWvm0XdAH3pjsnUKrNwpI8BkGxfIFvbaXouO0/1nUcJJZugnBal9+Wx2T18mW7uh0/XC37dcoklbL9P7D4bbAF9vGt+iGFXKndpwn3fvib5ZcpxWnbgj/taiZGYa06ywSHHpDGGydQaq3CcjYBkBViPrPEPsUSPLhwCS1GORZbLV+cU62B2H/qgDyBmkHJxYfHmcQYDJVudX5SjZ6jUcJlu9kNSnHyZbJlt9ZhL3ElcRYLLV+c0x2ZoC+jHH2UpoMNky2eq81HB3cQwBJludXxiTLZOt2pRismWy1Xmp4e7iGAJMtjq/MCZbJlsmW+0fFdtstWPFLeM2Aky2Or8/JlsmWyZb7R8Vk612rLhl3EaAyVbn98dky2TLZKv9o2Ky1Y4Vt4zbCFgkWxRvL1CgAKVOHRMTGNceN67kRtYbV/ZG1htRx/pjmy3bbB2bQXx1XEfAItl269aNtm7dSihn17ZtWypcuHCce14mWy6x5w6TlsmWydYd5iGPIfYQsEi2jx49opUrV9LcuXMJpe2KFStGX3zxBdWqVctqHVlnPRLKxqG8HgrMaxEmWyZbLfPE2W2YbJlsnT3HuH/3RkCTzRZ2ld27d9OCBQsIquWUKVPS559/Ts2bN9etXmqZMmUI5K6UdevWEQgzJCREFI+/fj06sTvuPXz4cEqUKJFFhPUk2xev3tLWC/fJx9uDquVVJzG22Zq+jvgSZxv56q0og5jJLwnlTutr9cvGfDl47RGlS+FNqT1fkb+/P3l4eFi9ztkNOF2jsxHm/hkBUwQ0ka102dmzZ+mnn36iY8eOGXpq1KiRUDHj1OuI3Lhxg969e2foAvfq06ePIPl06dJRx44dxYl2zJgxFBoaKlTbIFvc35LoRbYHroZR61kH6d2HJLfZU/vQsm7lKFWy6GTykrgr2UZEvREVaF6/fU9NimekrKmSOvK6bLo2PpDtzksPqP1fhwy1aVHcfXGXsmZxQCH4drMPGeZLsYy+tPSr8pTI07hovE1A6tTYXrLF5mHe/uv08vU7alAkPeVKk8zhEbGDlMMQcgdxBAGrZPvy5UvauHEjzZs3j06fPk0+Pj7Uvn17qlevHh04cIBmzZolHhWkqKd06tSJ0qZNS6NGjaInT55QyZIlacmSJRQYGChuA6IF6U6fPt0lZFt+9Da68/iF0b26VMpBg+rnd3uyvfkokj6ZvJfCI18Zxjq/UxmjZPh6vjtlX/GBbAsM2UiRr4zL4I1oXIjalc2qCl3xEZsp/HkM3mg0oG5e6loluqxebIo9ZPvgWRQ1nLyH7j55aRj6nPalqFo+x8wUTLaxORP43q5EwCLZLly4kMaOHUs4reHkCtUx7LXe3jGnOXwshw8fpnLlyuk27kOHDlGbNm1ox44dlDFjRgoODqa6devS3r17DWpr2JFhT169erXhvhinUjDuS5cuOTy27APWmfRRNgdON2WM/h4ZGUnwBMamJDYFY4CdMCAggH5ee96khFvmlElp13dVXTJELO5Q9ydOnNgl97O3kAMwU5Oo128p35CNJj99jTJ4QblN/g7tR86B603+3q1ydvq+rvHmzCWAKG4SEREh1Nla/R5w+W+bLtHk7cFGPUGrc2RQDYceAesHNmMwTcWG2DtXYmOsfM+4jYBFsv3666+F6rZ169ZUqFAhlzwpFrxmzZqJk+zAgQPFPaG2btmyJR05coRSpEgh/vbPP//QlClTjE7UjRs3Nhkj1NEgaUel3owT9PD5a6NuWgWmpb5Vsxj9TVqw3eEjlioI/bAmmLZdDjeB4NA3pRyFRdP1rsYEGwxb8ZdCpcw9UKVJRynqTYyZA+2+qZqZPgtMp3pJ9SnHKCLKuD5xz0qZ6PNS6TVh5sxG9ryPsdtCaOmJ+06ZQ3pVurIHszRpHDuZ23NPvubjRMAi2e7bt0/sOPPly2eEzv3792n//v1Uv3598tTZBrVp0ybq0aMH4d5YNCHSyVb+N7WTrdor1Mtmu+9KGLWZdcBgs0ufIjGt6F6e0qcw9op2R5vt+M3RNVXlUj5XalrU2fhU7qxPID6okbecv0ed5x0xQFQyqz8t7VaezJWc3XHxPrWfc9jQvnCGZLT8qwrklShu2myn7bhCYzZcMJoihTOmoDW9Kjo0bViN7BB8fHEcQsBqnC1OtD179jR6pNu3b1PVqlWFLTdHjhy6PS4+PKiLQeJwjpJEzWY7bNgwEY7kKpstxgK71ZLDNymptwd9Xi4reSZMaPLs7ki2b969p3azD9L+K2FivHDumtOhFGVL5RpVd3wgW+B2/+lLUeA9T1pfqpo3eiNoScKev6KVx24LZ7TiaTzitDcyVONf/HWIdl9+KB45k38Smv1FKcqbzrpXtiWMmGytzSL+Pb4gYBfZQjULle2WLVsoa1Z1BxF7AFq6dCmNHDmSdu7caVAXS/3AKSt58uSx5o2s9XnUyDY21GRv3r6jYSuP04GQCMron4Q6V8pOxTL70+u37yilj5fWx9GlXXwhW0fAcGac7aV7z2j+gRAKCYsknDb7BOWhufuuic0V3vWnJTJRmewpacr2K3Q0JJz8k3jQp4HpqXwe21Xaz1+9pZev3lKqZPrMISZbR2YVXxuXEFAl2379+lF4eDgdPXpUqJGzZ89ueKZXr14JL2SkcZQ7Jzn60FFRUVS5cmUR4tO1a1eT7q5evSribG/evCl+Q+jPiBEjrCbX0EuNrPX55GTbZ8kJWnX8tri0RFZ/mtY2kNL4usZJqM2fBwnhJ3JBqApCVmyR86FPac3JUHr+6o04Ebcvn82Wy0VbJluiu/fu0/DNN2n9mbsCE4RfjW9RTKihH0ZEUY+Fx0UML/6/X6281KOaNq/lsIgoqvjrdkJYjiRengnplcK+jPcuaTbQDvfZ0Luy2ZPpwoPR5O3t6UHZUiel4PvPKWGC91SvcAYqmCG5zXPA3AVMtrpByR25OQKqZAvHpMePHwuyxWkShCUJPEqRgAJqZITmuFqgOobTFv7RIrFFtguO3qPR641tXNZiM7U8j5Y2UPnlUPGe7lYlJ/1Q19j+bqm/y/eeUe0Juw2xomjbqFgGmvhZcS3DMLRhsiX6fskRWnL8nhFu8Gb+pmYeajnjgCBaufzROpAaFrF+8py45TL9vsU+b/te1XPTt7XymLzLvktO0MoPm0S1F72ye3kqnsXfpjnAZKsLXNxJHEbAohp5+fLlIqFEhQoV4uwjxhbZDl4XLOx1Srk+ur7TsXz7DqEnpqFKX1bOQQPraQ89UXOswuCv/VLfrGOQ2sMx2RIVGLKBkIFKLoFZ/GhF9wqU7Ye1JrB1rZKTBmjYGE3Ycpkm6Ei2SHqSe5Dp3JEPsG3ZLPRzY33ypPPJ1unLAd/ATRAwIVtMfqh0kyZNanP4hJs8k9EwYotsESqBjE1ygeoOROUKQQKC07eeGN1qettAqlPI+mlJugjep/BCVcqVUfXII2ECzY/BZEtUfdw2uvrQOClKnULpaHrbEpR9wFpShvj2rJaL+tXOaxXjqw+eU/Xfdlhtlz+9L50PfWbUblGXMlQ+p3FFL9hkCw7ZYLG/BkUy0OTWtmk3+GRr9RVxg3iOgAnZbtu2TdhMN2/eTOPHj6f1602D8yVM5HGv7opTbJHtmftR9NnMA0awwBbXs7o2W5yjeN4Oj6Q+i47S4ZtPyTNhAhreqBC1KWMcE2ztHrA3w+4sF9htt/ezLRkGky3RigOX6ZtVxurevzuVpsq5A2jK9mAau/GiAWbYXDf2qSxs5FpkT/BDGrr6DF19+JxqFUhHgxvkp0lbg2nZ0VvCkWlw/fwUVCAdDVp5WnhTp/X1ooF1ctMngerOjVXGbhf2WnMy/JOC9IUdtnu1/vhkq+UNc5v4gIAJ2V65coX+/fdfkZIRySQkhyS1h23VqpVRNil3BCS2yBY25SPXH9Hm8/fp1Zu3VCSTn3CKcZXoVc8Wp9vpO6+Ik1fuNMmEvbaAjQ4yTLYksnmdf/SO9l19RNAJIM1hqWwxWZPWnAqlM7efUKKECahZiUyaidae+WQtXePFu8+o9z/H6cLdZ+TtmZBKZPOnfcHRNuX2FbLTsIYF7Lmt6jVMtrpByR25OQJWcyO7+fitDi82ydbq4JzYQC+ylYYIsjWXwMHaYzDZRpMtV/0xnSlMtta+Hv49viBgQrbwQobNVosg1ZmtafG09KtnG1eT7boTN+jU7afk7eVFjYtndOoJxRJOepOtI++EydY82T6PeiPyViPxSJJEHtSlcg6h9nemWDvZOvPeyr6ZbF2JNt8rNhEwIdtu3brR1q1bNY2JbbbGMP29P4SGrD5j+CPWzDW9KlmNS3z37j0l1HmBdSbZ4pS7+NANuv8siirnTk2BWS2HgTDZqpMtyh7WnbCLbobHOE4VypiC/u1ZgRLaq0bQ8OW6mmxRkm/evmv04vXbD+UdY2zRTLYaXhg3iRcImJDtqVOnKCws2j4zf/58wofZvXt3o4f99ddfKX369DRjxgyrxdtjGyVXnmwR2yrVu5We21K4zcazd+mrBcfJqGO2AAAgAElEQVTENbCN/dW+FFXIZewdai9+ziLbd++JmkzdSydvPjYMbUiDAtSxYkziE+WYmWzVyRb5qhFepRTEMh+/8ZhuPIok/6ReNLRhAfrfkVu078pDsSmDo12+dL6EeNgnL15TjgAf+q15Uc2xr64k23tPX4ryjvi3JPM6lqYqeaLTXTLZ2vuF83VxDQGLNlvkKW7evLnI6iQXnHxxAj5+/Ljm5BKxBYwryVYtXrJFycz066dFTB7/3J2nVG+ScQ1gHGZODq1FyRMnchguZ5HtnL3XafiasybjsxQOxGSrTrbm4pjteflIy3jkxyBNJ2JXku2vGy7QVEX4WNrkiengwOjSfEy29rxtviYuImCRbCtVqiRSKCJfsVxQRB7pEpctW0ZFixZ16+d2JdnWnbibkN5QLv1q5aGe1U1rnv6++RJNVFTiwXUTWhYTtl5HxVlkay6Jwulhtck3sXpFGyZbdbJddzqUui885uirNly/qW9lUSTBmriSbBFutPDgDZMhScldmGytvS3+Pb4gYJFsv//+e1qxYoWoHYsi7Cg4/eLFCxo0aBCtWbPGUNzdncFwJdmeu/OEus4/arDBoTLM3A6lTeBB0vjBq2Jsu/IGf3csTZU/qNgcwdVZZKtGEMm8PenM8Npmh8tka95B6teNF2nqh6Ls0GwE5U9Lm88Zp3XUOg8ODaxBaZJbz73tSrL9Y9tlUXheLoFZ/EV5Sj7Zan2z3C4+IGCRbFG3FoXckY/Yx8dHVPg5d+6ceG4UlB8+fLjbY6An2V4Pe07fLT1Fh68/EhmUhjUsSO3KGScGQCGCpy9eU0q/5MIOCzkWEk6wz758806cPLDbV5MC6ZNT76DcItMPHGWC8ttf2NpZZItxD1hxWjhIQRIn8hC25vIWChx8jGT7OPIVDVh5htafDhU4wWu/WfEM1LlyTvppzTlhf0Xc8k+NC1HpbCkJzlK+3p5UZ+JuQhUfuWAzg98tScXcqWlBJ231iV1Jtkgd2lZW3hGl+TBfpBM4n2zdfgnlAeqEgNU4W5xkkSMZquNHjx5RxowZqVq1akK97O5hP8BIT7KtM2GXCPSXizIForLEHoi22fR9Jun4lO+vbI5UlMgjgaFeKH6vXyQ9TWkdaNerdibZYkBY/O8+fUnZU/lYTd34MZJts2n7RDk7a4JvCCfSAF9v0VTN7m+tD/xuS75qV5KtNHbUgkZuaNT2lQuTrZa3y23iAwJWyTauP6ReZIs6sLkHmaauVCaMV5LtyHXnadauq1ZhRHYptUorO76raleRd2eTrdUHkjX42MgWMbO5VApBmMPs25p5qFeNaLt+tXE76NrD57bAK9ou/6oclcgak5HKUgexQbbmxsNka/Or5gviKAImZIuwH6iKS5YsSVAj48M0J/nz5xd2XL0FNXNxbyTN8PIyLlL94MED4QGdJEkSTbfVi2zNVdJB3dHvZAnjlWRrzkFEPvjS2VNSzQJpaeTa8ybPNL1dCapTMJ2mZ5U3YrK1GTLdLkB4VI4BppV8zN3gx/r5qXOlHOLng9ceUauZB0xCyKwNDhWCsPHTIky2WlDiNoyAvghYLEQwevRoiwku9E5qgQLxcL5Cv5Bhw4ZRmzZtxH+HhISI4vHXr0dX0kFIEmzGiRJZDpPRi2xxz9azDgpbm1yWdi1PpbLHJHVQkq0y0QWuLZbZj0Y0LkRbz9+jXGl8qUGR9HQrPJIqjtlu8naPDa5JCOuwVZhsbUVM3/Y9Fh2jtaei7bVyUdpfEQazq381g30fbcdtukiTtwXbNKDd/atT5pTaNqBMtjZBy40ZAV0QMCFb2GXPnj0rTrY4RVo62ebLl0+3ky2csBBqVL9+fWrbti0VLFhQeD6nTBmtGkOsL060Y8aModDQUBF6BLJt1KiRRSD0JFtkeoL36I6L9ylrKh9R+UTpGBT+9BktOXKHXpMHNS+RidKlSEwDV56mRbLwBzhWta+QzWTccDqC85EkY5sXFX3YI0y29qCm3zXAf9rOqx+Sf7ynN69fU9X86ahFySw0cVswXbr7TNgvO1TIJuz0yMbVsGgGCn38kpYdvSmq86APCP6+5fw9evGhHm6RTCnolKx84sgmqOikXsFH7YmYbPV7z9wTI6AVAbex2Y4aNYpWr15Ne/fuJU9P43jNJ0+eCPJfsmQJBQZGOwyBaEG606dPdxnZWgP1YUQUNZ68l249jk6/h1CO+R3L0JpTd2jJ4ZtGl8/pUIqq5TX1NkZqO3g9o7ya5M0MG+CLV2/I14ZkF0y21t6Wa39XK0QQ9eYdNZ26j87eMa47LB8ZVMMPn0XR8mO3jAaM0JmkXp6UNWVSSuIVbcqJfPWGPBImNDolM9m69j3z3RgBcwhYJVuob/ft20e3bhl/7OiwZ8+emm2n1l4BslXBDpshQwa6c+cOFShQQPSfLl06Cg4OJvwOIoYdFzJ37lxauXKlIGhLoufJ1tozoCYpapPKJaN/Errz+KXhlCL91rZMFvq5SWFrXZI8A0/qZN40rW2gUWk2cx0w2VqF1qUN1MhWLQZVOShs2JSF5dGmV/Vc9G2t6OLyOBV3mHPYQNqI7/6rfWkyl26bT7YuffV8M0ZAIGCRbJcuXUoDBw4UDUF6SvsoiM7X13rGGi1YgxTLli1Ln376qXCKwok1MjKS1q5dS2fOnKGWLVsKW26KFClEd0i0MWXKFNq9OyblYcOGDU1udeHCBUHSrpDRW0Joxan7mm71SaEA+rGWqSpZfvGO4HDq/68xeafySUTruxYze49nL9+Ikw4qx4Bw3SE8y9XjCAgIsPm5pc2JppdnRyMlBlcfRtKIzSF0NjTCjt6I2pdOT90rRpsYUJR+z1Xj03GXchmoSznjTGSv3ryjRB6I/Y5WT6vNjVdv35GXaEMEp0C0dHYVIlfPDzng0ubdrpfAFzECNiBgkWyrV69OOXPmFKSm9Aq24R6amoJsp06dSjVr1hTt4SxVu3ZtkakKamWcbHHCxkIKUTvZwsarlCJFitClS6bJ3jUNSqXRlQfPadWJ2wR1b9rk3tRZloAfJ1tlHtgcAcmEShjOUHIZ07SwiKNN6uVhlhiQGlEtpePZ4bXFdXI5cDWMOs47YrDrNS6WgQZWz2jAy9zz4lQEezKKIWRJmZQ+ldmI8Tc9qs/gJIV3qNWD3N53I11n7wZDspE6en+16+Hlf/1ZAtpx+SEloAT0z+EbhNhTa4KiBCg2sOPiA6Omo5sWJuTdhuq40LBNJt3Au31muxJ04uZj2nHpAf174o4hpKhH5azUo2oOo/cBuzGcurBZS5wooSiIsfV89MaxTPaUwjehU6Uc5KOYd9bGb20OIfQHoWGSb4a1/vT+3d65ovc4uL/4j4BFsm3QoIEgv969ezsdCTg64WQKj2OIpDpGQg1krlLabOGpDKcqV9psQ8IiqcZvO0TtUUlq5E9Ls78oKf63/qQ9JvY3T4+EdG54bVGhZd2ZUHFKKJrJj47dfExwuMLCNqNtSaqSN3oTIZfpO6/Q6PUXTP6ulvQ/3+AN9PL1W6O2ODl3rl7Q7LtDJZYav+00yk7UslRmKpHVn35YfloQcGb/JDSxVXFCij175WOLs1XDafWhYOq94qLNEHp6JCB4vI9Ye05kIpMEGczwftRUzGgD5z2ok6FeVpNJLQrRJ4HRTlVwvCowdIPVxCuYCxv6VCYfb/Uc2PL73Hnykrr+fYRO344+cSO0CSFOSuE4W5unBF8QRxGwSLYTJ06kzZs306pVq0yclvR+3lmzZtGff/4pslVBNT127Fhx7x07dogdePv27Sl58uSx6o1srnjAxZ/rCqcUlBI7dSum9Bwwgkru0si6BrhuPoqkSr8ah/igVPi5n+oYHF2kxlDpNZi0xyh9X7ZUPqLAeJsyWQx94nRaeuQWk1eSIYU3+XgnojI5UlGPajkpfQrj0BBzz6PsKI1vYjo0KLpKiz3ysZDtoWuPRGhYBr8kFPrkJRXOmIKq54v2Maj123a69CDSHvgEUf3vyE2RBlSLIIUmHKi6zT8qyvSpSc7UPlQ8q78YJ3wBVp+4raVr+rZWHuqlUlhDefGn0/fTkeuPjP6s5l3PZKsJdm4UDxCwSLZQy5YrV45KlSqlqo4cPHiwbqpBJLLo37+/sNFCYCP+448/RAEECNTKOPXevBnt1YvQnxEjRlhVb+vpIIWE6nBqUUrJbP70R6tAajzFuG4n2n1dIzd9UzOP4RLETyKOUikoWICTiFJgZ/t68XHacPau0U9QQX9RLptwlgIp5/3RNLuV/AKEKu38rqpRH+aeR21enxhSi/yS2lf672Mg2++WnqSlR02dCKGOXdi5DOUfssGg4nfWuoFqUdlSJaW2ZbNSl3lH6Lis5rBe9+xdIzf1lc1nc/2qpZ1Uq+3MZKvXm+F+3B0Bi2Q7c+ZMccKUihAos0X9/fffutezxcIcEREhitOr2VOgOka8Lf7RInqRLeyao9adN5sQXs1rFCfWa6PrGw1z07l79OXf0Uk75ILrF3Yuq5rQ/5f1F2jGziuqjwsS/efLsvTjqjMmdmHlBVj086VLTs+j3lCWVEkFOYAk5AL1JBxjlNKzei7xd5yCOlbILsKatEp8J1tUe6o3aY9ZOCa1Kk47z92m5SetO88VyJCcUOvYHtn7Q3XK6JeErI3Hnr6la2Z9XlJkO7MmSG2KFKdy6VktF/WTZVvDb0y21pDk3+MLAlaLx4OsoE6Oq44EepDtvyfviNOlPXL1l/pGIRhz9l6jn/47p2ofgy0Mzk9KGbL6DCETlTlpVTozNS6WUdQNzZwyKR27EU77r4SZNE/p402Pnkc75aRIkogQ6/vPoZtCRQnxT+pFk1sXp8Grz9DVB+bz85bLkYoWf1lWMxzxnWxn7b6qmmpTAqhPUB5qXigFDVp3XTgrWZKjg2uKzZiWIgbyfuS+AzsvPaAv/jqk+f1IDeUbLWS2gk1fLv1q5SVsuqwJfAcmb79CkxVaoNals9Copsbhbky21tDk3+MLAhbJFqpaZHXq27dvnH1ePchWmQFKDQwc9JTnQS/PhHTp5xh7bf9lpwzEZg7Qq7/UM/EAXnAgRJxctQjKtk34rDg1mLTbZDzK67Ol9qH5HUtTh7mHKfh+dAgK8jTj9DJ333V6/eYdXb4fIcoDKmV3/2qC2JVy9eFzOn3rCQVm8TP8Ht/JNiTsOVUZu8Ps64GJoFCqBOTv70+9l5yk/1TSOOJi2Hr3/VBd9PPbpov0h8aUjSAwEJkkMD0UGraR8G+9pE6hdPRDnXwU8iiSSmXzFwk11KTf0pO0TEWdLrVVOvcx2er1hrgfd0fAItnOmTOHFi1aJOyozg79cRZQepAtCr2j4Ls5wal/cZcyBHXvyQ92MqhZx7coTquO3yKcNBD7KqXbs/Ssap7GaG/tdCvvEykAaxVIS98vO0k3wl8S0vtB5Cn+pPZV8gSI8ckFpxecYiDmbMzLupWjktmMq8z0Wnyc1py8Y+iqS+WcNKhePhHagRhtV4X+OGsuWep35q6rwsyglFals9AvTQuTlNSi37LTqtWdMD9Aypg/CPfC6VBNna82hkH181OXD4UM8DuuKzVyCz16/soiFGl8vUVCDFsFG0toRaoqMqCtOn6b+iw5YbG7CyPqiBrIkjDZ2oo+t4+rCFgkWzgoTZo0SaRITJUqlckzSvZcd354PcgW8Yad5hmHUFTMlVqEyIBoPymagXIE+Ih4yFVHQsjbMwE1CMxKbf48aCBfrRjt6FeVrj6MoIx+SSlvOl8RJ3nlfoTwKEbhbcTeTthiOW4YDltLu5YTua2loP1f1p2nGYpSf/CUhnOVUuQqSYRwlP9lq1GTJIk86NSwWh8SJET/tPvyA2o321R1uef76pTc43W8J1tggPd/PvSpyJuNMLGcaXwoIFl0nVqJbLddfEhdFDZ7bIYWdSkrVPo/rz2ndaoY2qEWctPAjCLu9sXrt7TwQAj9rFJBStnxvz0riHeGcdsq8L4HccrNS79vuUQTt5g6EMr7/vXTImKcTLa2Is7t4zoCFsl28uTJdPKksQON/IEnTJggnKfcWfQgWzzfhjN3CfbW8MjXwkFEXlYPv7f98yDtCY6uCITY2nkdSgmytVWweEnJFZBQArGUkgyol4/evH1PSJ5hSRBjOaxhASOyvfIgghr+sVckQZBkSptAGrfxokn91Pa4/pOY+Fx5IXTEfS7oVJbK5jA+1ZrbBMA5qGr2ZB8F2Vp6J/J0jXCS+/m/c2bDcmydM1J7bLKOXg+3aj6Q2m/qW1n4AsBMYY+s6lFBeNbvDQ6jFIk9xYbz2A3j0Ddlv0pvZj7Z2oM8XxMXEbCaGzkuPpR8zHqRrSUcZu66QqPWGSefULPh6oHlkR+DqMrY7fQ8yjiBhdR3Br/EtLRbecqQIrER2eL38MhXYnEFf1fKnUoUG280eS+dVMQGj2hUiNqVi054MHzNObHJkMuAevmpa+Xo+quSbD53z+TEht+296tKqbzeGsj2ZngkLT96S5yIWpXKTGmSJ9YDFrfvQ062yBwFNW9sSv50yWh9nypCXY1NodwhC+FqVfMEUNNp+8wOERvBVD5e9CDCNjU0Sku2KxtToUhJtpibS4/eFPnEaxdMS/nTJ49NmPjejIBuCDDZaoQSySqgmjt8PVwkKxjSoADhJAGBrQ42O6WoEe6K7hXo8PUw+kVBzhqHQf/1qihOzn/tuSZIsnS2lNSxYnbadekBeSfyEOkWpbzIcjWyWv+w7eUcuM7kJ3k8JH5X2g4LZkhOa7+uZHLd57MP0a7LMfbfRsUy0sTPihlstidDI0VhdOmsDu/Xpd3KOZSdSiturmqHZ4ODGNJp5koTE54GsvX2SU4/r7tIsG1GvVHfLLlinO3LZqKvKmentCljiAzzB9meUFsZanBr5gps1I6GGCetsDZ2ybwhVz3LyRbzDAQv+T2gP0fKTFobD//OCLgSAYtkC3vtsWPHzI4Hamat8a6ufCj5vfQ42b55+46Kj9hCz17G2LZAeEd/DBIhNOM3X6JJW01tVYgphFMU1MvpUySmg9ceUbgVpxVrOJ0eVpt8E1tPlycl1k8dEEDI5xyQzIv8kkYXoceihupEKPGmrFKE37tVyUE/1I1OrZdn0HoTu26xzH4EFaKabDl/n87cfiI8VpHQASI5SDWecZgu3n1mdFndQulFJSOlRES9EbHFT168If+kiahn9dyUyMOG4F5rQDrh90v3Iqjd7IOGkJnCmVLQki/LCeIF2X61/DIdvmYbQek9TMRJb+9dRtShTprU1Jsc5f42nb1HyLWN+WpOYEqBNsOaJPZMSL1q5BYnVCmblvwaOdn+ueeaUK/LBcR8dVQ9o7hu+FAcCXlEHgkSUL0i6akAn36tvQb+3Q0QsEi2SJ946tQpk2GuX7+ecuXKJVIrqn2wbvBchiHoQbbmElEgMxRUblALlhu9VdhTJYF36fHBNQ2el9Y8mrVghsxAPzcuZGi67vRd6r/spEi0USSTH/3esijlDIg+TYFs1x+9Qj2WXzTE9FbMnZoWdCpDDf7YIwjRnMBZB4nnIWpOL/CuxbMiXy/CS+DRPL5lMaFWVBOJbAsM32ZiT0T4EZzC5AI7da3fdxnCkfBb0cx+tNoMwWvBzhVtPpt5QJCUXLpVyUk/1M1Hx4NvUZM/zfs/aB0fYrEx70YoSEnL9diqLOhchoqk9TaQ7b4rYfTN/07Q3ScvCeUgb4ebFvNQ9o0NJhJoIGOaFDJm6f5QHf+64aKYp81LZKK+NXPTkNVnBVkjhej3NbJQ49K5VOca+j0vS2W64tgt+uZ/MTjC6x/aouKZ/bRAwG0YgVhDwC41MryUt2zZIurJJkwYXY7LXUUPsl13OpS6LzQ94SOWdHGXskJ9C9UXdubHb4RT4Qy+1L16HqFuliTf4PWiUpA1UQsRgrdprxq5qELO6JMi5PiNx9RkqnHpQFQY2vZtFfE7yBZZfORFE/B3JJO/qbKg4tSbL10y+qpqLkGekuBkjufaeOYuwTkKhQrQ9qsFR40epWTWlLTsq3KqjyeR7ZeLTguvZbnAMxUeqnKZt+86Df33rElfS7qWExVo3FXUUhTC0zgi6i1dfWBfKT21Zz0/oo4gx2rjzMf2ql0HcwPMH1I921fkScVHbLZagEDZV49quQThP4yIElWukEAFFbBQvm/bBetZstTGtqZXRXEt8nUrZed31ShrquhTeNHhm0y8p2EDBqGzMALujIBdZIuSdfXr16eNGzdSjhzGjjLu9rB6kC2ckQoO3aD6aMp8r8+fPxdEJ1evIxyj8LBNBHW0JcHuXC2frTK/MvowZ1M7M7w2JfP2FJmiAkeYOuHIvZ3lY/mtRVFqFhhdHxWCRA3dFhwToSwQEP3fnUoT7Kwj152nWSo26mu/1FdN4yiR7a2nb6mtTM2K0oNIIYlkDnJBnKnaoju5daCwKbqr1J2424CX1jEOblBAhPuYq96j1k/wqHpCxW7NK115LbKDNSiSwUC2C4/etZj5SsszoBrUn1+UpJQ+XuIZ2vx5gHBahmBTJjyUZdWKzPUJL2WYCcZtMiXb5V+VF2F2ELUNDeYE5gYLI+DOCNhFtvv376fPP//8oyFbvECo7WbvMfbKxd9xcvm3Z0XDO1YjW3PVdZBhSsryg8UEi1bxnzabzJc+QbkJKf/kgoIIKCSgFNTXffj8FSHdnlo+5er509C2D3VK5dfuH1BD2JUlaTFjP6GKjVykjcXo9edp+k5Th7Brv8C2ZmpXVSa1OHz9kXDiKm6mbN/1sEiqOta0MtLpDxsJd/2ggFfrPw8aNlXYRNx5bFkte310faF6hoMdUmRCTZwlZRKRkELNZoo6xcgQhlNgx7nq5fPk+OB1INsTVNmSFzBOtufuPqdJO0No74dwNUcwhS32r/alDF0gzSPGjzjxUWvPC82INcH8/qx0Zio7ShHT7eVB8FOQCtj3XHTMJAPX8EYFRVEOFkbAnRGwSLYoNHD2bIw6Dye2J0+e0LZt20Q1nqVLl7rzs4mx6XGylR6y2PBN9FiRAADev+OaF7VItiPXnifkz7Umf3csLRZRpEqUJF2KxLS5bxUTp6inL19T9XE7hSpPq/j7eNGWb6oQ1OKwIUOwGE9oWZxQpFwuaieIPGl9CbGZIMvm0/cbtUc6v+ltS6gOxZ4MUsCh24KjYjMCAkIhdMnhSuvzxka7x5GvafGhG8IpqlWZLII8zGVyQiYlJIZQE9g3Cw3daPKTPE5VbUOkvECtWtOJq3epyayjqqdpZWy3VgyxaVCT/VfDhAe6XGDzlSfS8Pb0EBWpMNeRO7r34uPidxRVGN+iqEjoIgmKaKDI/Y6L0eYIxJQPl8WEax0vt2MEXI2ARbIdN24cHT5svHtGTdmqVatSUFAQpU1rvfqHqx9IeT89yVZ5msDCBBVX8SwxzhnKky2cfdrMOkhYdKwJSuy1KpWFzoY+JZwPobLtVDG72WLdOEHM3x9Cka/e0sV7z1RPKfKE8pVzB4g0e1LC+bDnryh1Mi+TXMwYZy7YexVq76D8acXpGwI7HSohhT59IVTMyrJrR0LCBVHC0coespWwgmoSavit5++JxTfwgzrRGpbu8vvWC/epk5kTKBJ+IPuYmmBjm3/IRhEHK5fPSmURiU6evHhF5XOmFqQEb3hzgvcCgpbLmHVnaNou00QWmBeoVVsjfxpBkCB8LQLyPDm0ltmmUCsj3AlECSc9lALsNPeIqAqUN60PNcjvR2XzZSHEYEMy+ycVphhJS3Lh7jMxZ5H325wg3he1ouFtHRYRRYUy+rm997oWbLlN/EHALjVybD4+YkdhD9WaZ1cL2SJncOiTFwQygoOSJUFFnV2XojNFNQvMKJLtgwhevH5HtQqmpdcvXxjZbD//65CIgZULbKrWFjI4RaF0nlKQyQpqRyw+lfMEGJyZEHpkadGV+kEOXeTStSZqxQ8WdilLFT54KZu7/vbjF9T2z0N07WG0QxDsdtNaFqRiWfw1vzN538hO1PbPmNhcqNv/17WceH53FDjKwXkJ70aaS7B7rzx8jXySJCZPT09BMthYIYTKkijnjlrcdqGMKSx6lstPwiDuaTuu0Lbzd+n0HeMQLEewtLRpUPaLk2uHvw4ZvNKr5wugQUFZqdfyS3Tug39AwQwpaEGn0vTizTuRmU1yLkN5yEVdygj7sFxwEl4ty8mN3+CsNbdDqTihDXEEe7427iDgNmS7efNm6t69uwlyZ86cIW9vbwoJCRHF469fj1axNm/enIYPHy4yE1kSS2SLeNMWM/eLFHeSLEJN2VymeaDV7nEr/AW1nLGfQDAQEMDstkWoZBY/sSF4/RYewaZJI+DwhHhLa6fdgfXyE+ykkqjVn539RUlCLmOMpeKYbVZnHkKDtn7wWLbWGNV+kKABJwyQB2JnrYlaZaMiGX1pSedSdpGtWl1U2Pdgx3YnEXNpxn5DJiZgtrBTaSr/IdZYnkFKy7iRWxmZwhwVeI9nSJGEfJN4isxdZ+2slas2DoQ14aSKPOFaBCdyJElROoOlS+5Nd58am0NgX0Zq1P9OxRS2wD2UamNUUIIdV02snbi1jJnbMAJ6IWBCtufPn6dBgwZp6l/P4vGbNm2i/v3706pVq4zunTVrVrHYd+zYURDYmDFjKDQ0lFD+D2TbqFEju8kWJcxQykwuOI0grk+LDFx5hhYdNFbHwbllXffSYqxIGpH3x/UmXcF78sajSNUqPPLGUOl9WyvGMarwsI307KWxag9OKA2LZBCkDAeddjg1WHBthVoXcbTOkspjt9ONsGh1oFzOD61uM9kibCmXSoYrdwz1mLjlEv2uSMIvr09sK9kqKyg563050m/wyLoim5lWgbNY+dHWN4ToD/P62sPnJmUCkShkjcwh0Vqmq4sj6ojQPBZGILYRMCHbK1euiGLxkkBte+TIEWGnVapuR48erVtSC6bYxcMAACAASURBVJDt4MGD6eBB0+T9cMoqWbIkLVmyRFQggoBoQbrTp0+3m2zNeRibK3OnvFGN33YSEvwrJaNfYrr9+KWwh4ZFvDJJ5GBr3mQpMUL2H9aaTTKfJWVS2tCnMtUYv5NCLXjAwmZbTVEaTc9J2HneEdpy3jizELJX7fq2os1ki3GpPTMyEn1b09g7W89nsKcvtRzS6EeqT6yVbBEms+9qGE3aclm1IpM9Y3P0GpgCvDwSGJXj+6x0FhqtKARv7T7mNp9Q+UK1LhfYsnGyVcZl46Q+pllMXPbCgyE0aKV6rWdomrAhUPOQtzZW/p0R0BsBq2pkOEi1bt2aDhw4oFpmT68BgWx79OhBTZo0ocSJE1OpUqWobt26wsYVHBws/nvv3r2GknFz584VSTVWr15tN9mqpVmE0xMWSAhiSZ++fCMcLUB4CNWRCzLvrDh2Wy8ILPaDKjwnboTTqhPGajX5RWqepLBvwWMav0EVLGWGctagcbqGaj0mlxbRzFaFqFKeNHaR7ZLDN+n75TFZzOCxuu7rSiZ2O2c9j9Z+1eYSFvuLP9el2buv0oPHzyhXen/6rHRMEn5l332XnFCtdat1DM5qBy90+A/ASx6mkeypkxqVybPlvsoNLlIt9q+embouOS80QRCU70PObKIEQjUvOYlBLQyHRHnOaWhx4BkPhzyl/NGqODU044Bmy5i5LSOgBwJuQ7ZIC4k0kH5+fnT79m1avHgxtW3bloYOHSryM7ds2VKcsFOkiM7K9M8//9CUKVNo9+7dBhygalYKfkdcsJo8f/WWvlhwlq4/iomFHN0wFwXlTUXdlpynIzejEzpAcqZOQou/KGzkuXv+3nPqvPicYZHQ44WY66NO/tQ0uFY2+u7fYNp3zXIZM2UfR/qVMekWdWrXngsT+WVbFE9Lybz1U7XdDH9J689He19XyelHuQOik1bYm23sxK2ndOjGM5HBql3J9Fa9TFF72dbTDBbtsDDrHuPm3g/mwYnbxk5HmEvzDoUS5okkVXL502+NTU/lx289oy7/2F7LVs8517NSZpq8+6Zql9t6lqDkipzcUPOvPHmfnr16S6mTetLdZ6+ock4/ypfWvNcwOt9zNZzO3Y2kpIkSUqsSaZHujJ69ek8rTkZnn2paNID8kkT7YjyLeiP+jnmKvyNmWE02XQgT37GPlwdFwlkxXyrK6m+9olTq1NrszXrizH19nAi4Ddkq4UcM78CBAwk2ZDhF4WS7b98+CgiITiWodrK9ceOGyVusUaMGXbhgXP5O3ghOG3P3hYgiAyjpBY9H5HutPXGPSV8D6+ajThWNg+cR7zpvXwhN3BqsuY6osmOcPkc1Lkhf/3PSrOoQMZnY4YNwvg3KTRO2RhcS0CJXRhrboA9ceyQ8hqXTJ+zU/+tSmgpkiEkvqaVfrW0iIiKEIxsc3VwhSLJvj7x9a18lHoS2tPvLNMHE5+WyipKGStn/QzVK42uMxaStwTRxW7DFYSvjU+15RnuvOTkkSGQmkwSxw82mH1CtyTuoXj7qWEFbkglgjiQb2GTHhtg7V2JjrHzPuI2A25Ltrl27qFOnTnT69GmKiooysdkOGzaM7t6965DN1tyrg80RtkelWPKCRRrCPZejQ4LkguQGiBOV+ywh9hWVdZCjOGkiD2pTNgshITviWg9eC6e/9l4T4USWpFXpLATvZGspIBGni5SAcqn863aTRRKJBaSyb0hQMa1NCdXUi/ZMd0fibO25n6uvmbP3Og1fY5rLGSpSKZxFPqY1PStQ4UzG5HLy1hNqNNl0gyddh5AnJB5BAn9rgjkHYrz/THvCE0t9Ih/1P1+WEwULVh6PNpvI47fVrk2SKHreF8qQXGS8kqt+5e25eLy1t8m/xxcETMj20aNHwjYqCeylU6dOJZAbElrIpXbt2uTlpV7pxVaAFixYQHnz5qVChQqJLFV9+/YV9tr58+eLrtq3by/ur6c3srkxIvl+gSEbTE6qK1FdRJbAQn79uTtPqdWsA4bMOLDvNi6WkTpUyC5OzbBVodIOkvz/2KCA2cVH6hMpHlGuzt8nkSqJI152QL18NGT1GVpwwPhEj/hNqPgqZ0tG/RsWM3lMtexQykZfVc1J39fJZ+trVG0f38kWp7zAEaZpNld0L09NpxoXYIeGAvmrpfSDcsDMOewh8xeqNaGOMKrerD9zV2Qyw+kYznYFM6agg1fDRFKTGvnSUu+aeYSK9teNl8SmLV3yxKLsH8hPkkz+Sah9+Wx072mUanYz1KtN4pWQimRMQX1r5iV4W0/ebvnkbW6y5EjtQ9sUlZ2ktky2unxi3EkcQMCEbI8ePUqfffaZpqHLbaiaLrDQaOzYsTRz5kxDC6SDHD9+PGXOnFn87erVqyLO9ubNaJsSQn9GjBhhley1JLVQG9buyw9F7ll4SSKl4YhGhQgl7iwJYi3XnrghbFD1i2fVLfFCjgHrRNYguXSvmov618kr/gRHru0X74sEEi1KZaaqeQJE+I+54vEN/9gjCoVbEoRebOxT2dHXKq6P72SLZwT+Xy04JlT9UMtPbRMovL5Xn7gjToSYGyDNqa0DqZyFxCAgxbO3n4gkIIidjnz1hkpm9bcpxEbtpSFuFylDkWAjf9qk1L1yNsqQ2o8mbLkkiloo5fLIuiIxhCRa5oylyXLupzoihaVSmGx1+cS4kziAgAnZvnr1SrOjCNI12uv0oobNy5cv6f79++Tr60v+/uoJFKA6Rgyr1qL19pKtND7Etfp4e6imNFR7BrVCBI7OAxR4l1d4gfMPPHLzp/c127Ulsj1x87Eocq6M2ZV3hkQFqH2qh3wMZCvhhBSVSq91vIs79x5QuoBUoo5sbItUYg+1qBFeU23cdkJOZ0kQdoOsUHLpMPcwbVeUz8MmVGu1IiV5S30z2cb2bOD7uwoBqzZbVw3EWfdxlGxtHZczyBZjQG5ZnEaxkCMpBlLaWRJLZIvrcFLG6R22tethzwmZn+Qyp30pqpYvja2Pr9r+YyJbc4BpjbPVBXArncjJFk2RAQ3JWZBjO2tKH2qv4tyEk3uHOcZOYKj0gzKJ2LQhC1TIo0jKmsqH6k3cbVQgQ6pUpDYsJltXvHG+hzsgwGSr81twFtnaOkxrZKvsDzmXD16LDgWqkjeAKuWOKSBv672V7ZlsidyZbLW+X+Tk3nnpgTjNVsqd2mze4QfPoujv/dfp5et3oui7JfMLk61W9LldXEeAyVbnNyiR7bJTD2n18dvC1oakEsh840qxlWydOTYmW8fJFqUUp+64Iuy5SDKBUyRiUZuXzCyIzxZRnmxtuVbvtky2eiPK/bkrAky2Or8ZkO2fe2/Q79uM69eOalKYWpfJovPdzHfHZOsyqDXdyJGTLU6SQePVU4Pi5ou/LEvlZDVfrQ2IydYaQvw7I6A/Aky2OmMKsi05ZjchfEguKIX2X6+KOt+NydZlgDp4I0fI9vD1RyIloTlBEQpUiNIqTLZakeJ2jIB+CDDZOoAl4isTJ0polEIOZFt05E4R5yoXPUNptAyZT7ZaUHJdG2tki5Ah1DhO5eNtkkwEyVKQNMWcdK6UnX6sb5y4xNKTMdm67r3znRgBCQEmWzvmAhJYdJp3mEKfvBRXV8+XhuCZCQHZjt4YTPMP3TLq+ZuaeQh1bF0lTLauQlrbfSyR7aCVp2nhwejEJMj8NOvzkkaxuG/evqcyv2ylsAj1jFBoX7NAWm0DQb7hZ89ECBJCf2Jb2GYb22+A7+8qBJhs7UC69oRddPGucdL5IQ0LinywkoPUr1uv04KDN0SGH6RMtEXNZ8eQTC5hstUDRf36MEe2asXP/ZImohNDahnd/MLdZ/Tz2nMiS1TetL6itGNKH28xr5DG0RZhsrUFLW7LCOiDAJOtHTiqpTuUVHlxNfTHDhg0X8LeyOa9kZGWc+JW0wxOUrlE/6ReNPGz4lQ5j20ex5ZeDpOt5qnLDRkB3RBgsrUDysLDNol8x3JJnjgRnRpWy3Cy1Zrhyo7ba7qET7aaYHJZI3Mn25m7rtKodeetjuPAgBqEWr56CJOtHihyH4yAbQgw2dqGl2j926aL9IdKObQ931cnf693Ii8xk20MsHyyNX+yhSMdqv2cvRNTO1ltSvarlZd6Vs9lx2w1vYTJVhcYuRNGwCYEmGxtgiu6MdR+UP8p5eTQWuT57hWTrQIYJlvLSS1QpGDBgRCRp/jkzXDafvGBydz6pWlhQllFPYTJVg8UuQ9GwDYEmGxtw0u0Do98RRXHbKfnUW8MV6OSy+IuZVmNrIInk632DFLIU11z/C5RbUqS3GmT0cY+VSghvO10ECZbHUDkLhgBGxFgsrURMKk5SpYtOXxTEG8GvyTUs1ouER/JDlKmgDLZaidboHflfgQtP3ZL1KxF3G23qjnJR6U8nZ1Tl0N/7AWOr2MEHECAydYB8NQuZbJlslWbF9aSWug8DS12xydbV6LN92IEohFgstV5JjDZMtky2Wr/qDiphXasuGXcRoDJVuf3x2TLZMtkq/2jYrLVjhW3jNsIMNnq/P6YbJlsmWy1f1RMttqx4pZxGwEmW53fH5Mtky2TrfaPislWO1bcMm4j8FGQbdx+RTx6WxE4duwY+fr62nRZZGQkFS1a1KZruHHcR+Ds2bPk5eVl04OEh4dT6dKlbbqGG8d9BC5fNk2rastTxXuytQUMPdouXLiQXr16RR06dNCjO7v7ePnyJTVv3pzWrFljdx96XTh27FgqUqQI1a5dW68u41w/bdu2pXHjxlG6dOlifewzZ84kf39/MT9iWy5dukQTJkygqVOnxvZQ3P7+sY1Vq1ataNKkSRQQEOByrKZNm0Zp06alpk2buvzep06donnz5tFvv/3m0L2ZbB2Cz/RiJltTTJhsiZhs1T+02CYQnT9/p3YX21gx2TLZOnWC29o5ky2TrdqcYbJlsrV1LVG2Z7Llk62jcyheXc9ky2TLZKv9k45tAtE+0thvGdtY8cmWT7ax/xXIRsBky2TLZKv9k4xtAtE+0thvGdtYMdky2cb+V8AjYAQYAUaAEWAELCDADlI8PRgBRoARYAQYAScjwGTrZIC5e0aAEWAEGAFGgMmW5wAjwAgwAowAI+BkBJhsdQAYKec8PT1Ve3rw4AElS5aMkiRJosOdzHfx5MkTQiILBH6rCRJtPHr0SPyeAIV3nSTAAuXk3r17J+7l4eFhcidXYeKkR4xz3b5//57evn0b63NUAg5zJGHChOIfFvsRQKnE169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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = px.scatter_matrix(\n",
    "    GA[['pm25pa', 'pm25aqs', 'rh']],\n",
    "    labels={'pm25aqs':'AQS', 'pm25pa':'PurpleAir', 'rh':'Humidity'},\n",
    "    width=550, height=400)\n",
    "\n",
    "fig.update_traces(diagonal_visible=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "The relationship between humidity and air quality does not appear to be particularly strong. Another pairwise measure we should examine are the correlations between features: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "tags": [
     "hide-input"
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     "data": {
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       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>pm25pa</th>\n",
       "      <th>pm25aqs</th>\n",
       "      <th>rh</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>pm25pa</th>\n",
       "      <td>1.00</td>\n",
       "      <td>0.95</td>\n",
       "      <td>-0.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pm25aqs</th>\n",
       "      <td>0.95</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rh</th>\n",
       "      <td>-0.06</td>\n",
       "      <td>-0.24</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "         pm25pa  pm25aqs    rh\n",
       "pm25pa     1.00     0.95 -0.06\n",
       "pm25aqs    0.95     1.00 -0.24\n",
       "rh        -0.06    -0.24  1.00"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
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    "GA[['pm25pa', 'pm25aqs', 'rh']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "One small surprise is that relative humidity has a small negative correlation with the AQS measurement of air quality. This suggests that humidity might be helpful in the model.\n",
    "\n",
    "\n",
    "In the next section, we derive the equation for the fit. But for now, we use the functionality in `LinearRegression`  to fit the model. The only change from earlier is that we provide two columns for the explanatory variables (that's why the `x` input is a data frame):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "y = GA['pm25pa']\n",
    "X2 = GA[['pm25aqs', 'rh']]\n",
    "\n",
    "model2 = LinearRegression().fit(X2, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "The fitted multiple linear model, including the coefficient units, is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PA estimate = -15.8 ppm + 2.25 ppm/ppm x AQS +  0.21 ppm/percent x RH\n"
     ]
    }
   ],
   "source": [
    "print(f\"PA estimate = {model2.intercept_:.1f} ppm +\", \n",
    "      f\"{model2.coef_[0]:.2f} ppm/ppm x AQS + \",  \n",
    "      f\"{model2.coef_[1]:.2f} ppm/percent x RH\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "The coefficient for humidity in the model adjusts the air quality prediction by 0.21 ppm for each percentage point of relative humidity. Notice that the coefficient for AQS differs from the simple linear model that we fitted earlier. This happens because the coefficient reflects the additional information coming from relative humidity."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "Lastly, to check the quality of the fit, we make residual plots of the predicted values and the errors. This time, we use `LinearRegression` to compute the predictions for us:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "predicted_2var = model2.predict(X2)\n",
    "error_2var = y - predicted_2var"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
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    "tags": []
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = px.scatter(y = error_2var, x=predicted_2var,\n",
    "                 labels={\"y\": \"Error\", \"x\": \"Predicted PurpleAir measurement\"},\n",
    "                 width=350, height=250)\n",
    "\n",
    "fig.update_yaxes(range=[-12, 12])\n",
    "fig.add_hline(0, line_width=3, line_dash='dash', opacity=1)\n",
    "\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "The residual plot appears to have no clear patterns, which indicates that the model fits pretty well. Notice also that the errors nearly all fall within –4 and +4 ppm, a smaller range than in the simple linear model. And we find the standard deviation of the residuals is quite a bit smaller: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8211427707294048"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "error_2var.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "The residual standard deviation has been reduced from 2.8 ppm in the one variable model to 1.8 ppm, a good size reduction. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [],
    "user_expressions": []
   },
   "source": [
    "The correlation coefficient can't capture the strength of a linear association model when we have more than one explanatory variable. Instead, we adapt the MSE to give us a sense of model fit. In the next section, we describe how to fit a multiple linear model and use the MSE to assess fit. "
   ]
  }
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